The change means Mr Gove, who will keep the title of Chancellor of the Duchy of Lancaster, will be Lord Frost's new boss at the Cabinet Office.
'Not accountable'
The peer said Mr Gove had done an "extraordinary job for this country" in talks with the EU over the past year.
In taking over from him as chair of the EU-UK committee tasked with implementing the Brexit deal, he said: "I stand on the shoulders of giants."
Labour's shadow international trade secretary Emily Thornberry tweeted: "So we've finally got one minister taking a grip of the problems with our post-Brexit trading relationships with Europe.
"Someone who has never been elected by anyone in this country, and won't be accountable in the House of Commons to any of us who have."
This appointment again shows that Brexit didn't end with the signing of a trade deal.
While the UK is no longer a member of the EU, negotiating with Brussels and member states will preoccupy this and future governments for years to come.
Since the start of the year (and the end of the transition period) serious tensions have flared up between Westminster and Brussels over trade disruption between Great Britain and Northern Ireland and vaccine supplies.
Other issues, such as the City of London's access to EU markets, remain unresolved.
Lord Frost will now be the UK minister responsible for co-ordinating all this and it will be a full time job.
Rather than responsibility for the EU being shared between several departments - such as the Foreign Office and International Trade - the decision to put Lord Frost in the cabinet and in charge of the Withdrawal Agreement Joint Committee gives him huge clout overseeing policy.
It also takes a lot of work away from Michael Gove and means there will be a single minister responsible to parliament for EU relations - although of course he'll be answering questions in the House of Lords and not the Commons.
Speaking last week to a select committee, Lord Frost said the UK's relationship with the EU since the trade deal between the two came into force at the start of the year, had been more "problematic" and "bumpy" than he had expected.
He said he hoped we would "get over this", but added that it was going to require a "different spirit" from Brussels.
Lord Frost - who is said to be highly rated by the prime minister - had been due to become the UK's new national security adviser earlier this month, but was replaced days before he was due to start.
He will be the co-chair of the UK-EU joint committee, which was set up to resolve differences arising from the treaty which took the UK out of the EU in February 2020.
Northern Ireland tensions
Since the UK left its Brexit transition period in January, this committee has mainly focused on overcoming trade tensions in Northern Ireland.
Unlike the rest of the UK, Northern Ireland is continuing to follow EU single market rules on goods.
This provision, agreed as part of the withdrawal agreement, was designed to get rid of the need for checks at the border with the Republic of Ireland.
But it has meant checks had to be introduced on some goods travelling between Great Britain and Northern Ireland.
Since the new rules came into force, there has been tensions at ports in Northern Ireland, with disruption to some food supplies and online deliveries.
Lord Frost will also become UK chair of a separate committee being set up to oversee the post-Brexit trade deal he negotiated with Brussels last year.
Rules on meeting people outside are also likely to be relaxed in time for the Spring.
While current rules allow Brits to meet one person outside, the rule of six is likely to be restored.
It's also expected that the rules will be relaxed so that Brits will be able to sit on a bench and relax with friends - rather than be ordered to keep on moving as part of the exercise rules.
Outdoor sports such as tennis, outdoor swimming and golf could also be reopened in the coming weeks - though close contact sports may have to wait a while longer.
Schools will reopen from March 8
Shops could be next
Non essential-shops are likely to open after schools.
Government ministers are considering allowing families from the same household to go on holidays from the Easter break.
This means Brits would at least be able to enjoy a holiday in England - though international travel is likely to stay on hold.
Bookings for popular destinations across the UK are already filling up, with many in the hospitality sector praying for a bumper season to end their Covid woes.
But the plans would only happen if the crucial R-rate remains low up to April 2.
No more tiers
The PM hasn't yet made any firm decisions, but has said he is looking again at the tier system.
Mr Johnson has previously hinted that he may lift restrictions across the whole country - in the same way as the first lockdown.
Instead, a tier system could still exist but it would apply nationally.
Brits could be allowed to drink pints outdoors from April
Social distancing to stay
There is no indication that social distancing will be scrapped in the coming months.
Ministers are under huge pressure to reduce all social distancing rules after vaccinating the over-50s, but health experts are more skeptical.
A source told Sky: "This is the killer argument and no decision has been made. A lot rests on it for some businesses - the difference between being viable and not."
A second senior Whitehall source confirmed no decision had been made on the "one metre plus" rule.
Lockdown lifted in stages
Brits shouldn't expect an overnight return to freedom, as lockdown is likely to be lifted cautiously and in stages.
The PM warned the lockdown lifting will "be based firmly on a cautious and prudent approach”.
Last week’s encouraging data showed just one jab of the Pfizer vaccine provided two-thirds protection against the virus in boosting hopes of a swift return to normality.
And Government scientists at Public Health England hope the Astrazeneca/Oxford jab will have similarly positive results to present ahead of the weekend.
The impact that the vaccine has on both hospitalisations and transmissions is likely to have a significant influence on whether restrictions can be eased sooner rather than later.
What we don't know for certain
Specific dates
As of yet, there are no specific dates that the government has issued for the easing of lockdown apart from the reopening of schools on March 8.
It is worth noting that the PM has continually stressed that the dates for reopening are flexible.
And with the discovery of highly transmissible new strains in the past few weeks, ministers have pointed out that all dates are subject to change.
Should a spike in cases occur, the PM could well delay the reopening of industries such as hospitality or non-essential retail.
Foreign holidays could be off the cards
Brits were left confused last week as cabinet ministers issued wildly different answers on whether foreign holidays were possible this summer.
Transport Secretary Grant Shapps warned Brits not to book a holiday - despite Matt Hancock claiming he had planned a trip to Cornwall.
Mr Shapps said travelling abroad would depend on "everybody having their vaccinations” in the UK – and potentially abroad.
When asked if travel restrictions will stay in place until everyone has had a vaccine, he said: "Yes."
While the UK has surged ahead of other countries in giving out the jab, many nations - including the EU - have seen a slower rollout hampered by production delays.
Vaccines minister Nadhim Zahawi hinted venues that will need to mass test visitors won't be allowed to reopen until almost all the population is vaccinated.
And he also refused to rule out social distancing measures, like mask wearing and the one-metre rule, carrying on well into the future.
However, he has earmarked fast lateral flow tests as a key way of getting larger venues open to the public again once lockdown is lifted.
Similarly, there is no current date set for the reopening of gyms or other close contact services, such as haircuts.
But this has sparked controversy in government, with one insider telling The Sun: “People are getting fed up at not being able to go for a haircut. It is about improving how people feel about themselves.”
Brits could enjoy a staycation later this year
Working from home to continue
There has been no date proposed for Brits to head back to the office.
Yesterday, The Sun reported that Brits would continue remote working even as some lockdown measures are eased.
It’s expected the “work from home if you can” message will remain in place for the foreseeable future.
No crowds for live sport yet
Though limited crowds were allowed to attend live sport in the Autumn, there is no date in sight for when sports stadiums can reopen fully.
Millions of tests, which return a result in half an hour, could be used every day in settings from workplaces to football stadiums.
Sports fans could also be sent Covid tests along with their tickets so they can watch major events including the Euros and Wimbledon again this summer.
But with social distancing to remain in place in some form for many months yet, stadiums are unlikely to be completely full for a while yet.
Brits will never go to work with a cough or cold again, says top health boss
The prime minister joked that he felt "like OJ Simpson" as he struggled to put on a pair of gloves during a visit to a coronavirus vaccination centre.
Boris Johnson was attempting to pull on a pair of blue disposable gloves at the facility in Cwmbran, South Wales, when he referenced the infamous moment in Simpson's 1995 double murder trial.
In what became one of the defining images of a case that made headlines around the world, the American actor and sports star was unable to put on a pair of gloves thought to have been used in the killing of Nicole Brown Simpson, his ex-wife, and her friend, Ronald Goldman.
Image:OJ Simpson (centre) reacts after being found not guilty in his 1995 double murder trial
The gloves became a focus for Simpson's defence team, with lawyer Johnnie Cochran telling the jury: "If it doesn't fit, you must acquit."
Simpson was cleared of murder after a highly-charged trial in Los Angeles County, California, that divided opinion in the United States.
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Two years after he was found not guilty, Simpson was found liable for the deaths of his ex-wife and Mr Goldman by a jury in a civil case.
He was ordered to pay their families $33.5m.
Simpson was later convicted of armed robbery in 2008 and spent nine years in jail before being released in 2017.
The Duke of Edinburgh was admitted to hospital on Tuesday evening "as a precautionary measure" after feeling unwell, Buckingham Palace has said.
Prince Philip, 99, was taken to the King Edward VII Hospital in London, the statement added.
A palace source told the BBC the duke travelled by car to the hospital, where he was admitted on his doctor's advice.
He had been feeling unwell for a few days, but it was not related to coronavirus, the source added.
They said the duke - who celebrates his 100th birthday on 10 June - was "in good spirits" in hospital, where he is expected to remain for a few days of observation and rest.
A No 10 spokesman said Prime Minister Boris Johnson sends his "best wishes" to the duke as he "undergoes a few days of rest in hospital".
The palace is pretty protective of the privacy of members of the Royal Family when it comes to health issues; those hoping for running commentary are invariably disappointed.
But palace spokespeople have gone out of their way to emphasise that this was not an emergency admission and that it was precautionary.
The duke has been in and out of hospital a bit over the past few years, most recently just before Christmas in 2019 when he had treatment for a pre-existing medical condition.
But overall his later years were marked by his health and energy; he gave up smoking the day he married the Queen; he has never drunk heavily and was for decades a keen sportsman, driving himself constantly to stay fit and strong when others might have been tempted to take it easy.
The last time he was seen in public he seemed in good health, standing unaided - and he walked into hospital on Tuesday evening, having travelled there by car.
In April 2018, he was admitted to the King Edward VII hospital for a planned hip replacement, and was discharged after nine days.
He waved to the media as he was driven to Windsor Castle to recuperate, before attending the wedding of the Duke and Duchess of Sussex the following month, walking unaided.
His Land Rover Freelander landed on its side after colliding with a Kia as he pulled out of a driveway.
Prince Philip was unhurt, but he visited hospital for a check-up. The Kia's two passengers required hospital treatment and he later wrote to one of them - Emma Fairweather - who broke her wrist in the accident.
Buckingham Palace later announced that "after careful consideration" he had voluntarily surrendered his driving licence.
Last July, Prince Philip and the Queen attended the private wedding of his granddaughter Princess Beatrice in Windsor. It was believed to be the first time the couple had attended a family gathering since lockdown began.
The Duke of Edinburgh has been admitted to hospital as a "precautionary measure" after feeling unwell, Buckingham Palace has said.
A palace spokesperson said the 99-year-old is "expected to remain in hospital for a few days of observation and rest".
A royal source said Prince Philip does not have a coronavirus-related illness and walked into hospital unaided on Tuesday evening.
The source added he travelled there by car and was not an emergency admission.
Buckingham Palace said in a statement: "His Royal Highness The Duke of Edinburgh was admitted to the King Edward VII Hospital in London, on Tuesday evening.
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"The Duke's admission is a precautionary measure, on the advice of His Royal Highness's Doctor, after feeling unwell."
Philip retired from public duties in 2017 and rarely appears in public.
More from Duke Of Edinburgh
He was last seen in public in July 2020 when he transferred his role as colonel-in-chief of The Rifles to his daughter-in-law Camilla, Duchess of Cornwall.
He has been staying with the Queen at Windsor Castle since coronavirus restrictions were first introduced last year.
Philip has suffered a number of ailments over the years, including being treated for a blocked coronary artery at Papworth Hospital in Cambridgeshire in December 2011.
He was later treated for a bladder infection in June 2012, forcing him to miss the Queen's Diamond Jubilee celebrations.
Exploratory surgery on his abdomen followed in June 2013 and he began to use hearing aids by 2014, aged 93.
He later pulled out of a Battle of Jutland anniversary event in June 2016 citing a minor ailment which was followed soon after by his retirement from public duty in 2017.
Philip was involved in a car accident in January 2019 but was unhurt and did not go to hospital.
He spent four nights at the King Edward Hospital in December 2019, where he was treated for a "pre-existing condition" and was later discharged on Christmas Eve.
Earlier this month the palace confirmed the Queen and Prince Philip had both received their first dose of a coronavirus vaccine.
It is understood the Queen decided the information should be made public to prevent inaccuracies and further speculation.
Boris Johnson says it is "absolutely right" to take a "data not dates" approach to leaving lockdown, stressing England will ease measures "cautiously".
The prime minister said he will set out "what we can" in a road map for easing restrictions on Monday.
"We want to be going one way from now on, based on the incredible vaccination rollout," he said.
It follows a call from scientists for a data-led approach to lifting measures.
Speaking at a mass vaccination centre in Cwmbran, south Wales, Mr Johnson said relaxation of measures would be done in "stages" and that the reopening of hospitality was one of the last things to return after the first lockdown.
"You have to remember from last year that we opened up hospitality fully as one of the last things that we did because there is obviously an extra risk of transmission from hospitality," he said.
Asked whether he agreed with a data-led approach, Mr Johnson said "I do think that's absolutely right" and said the relaxation of measures will be "based firmly on a cautious and prudent approach", in such a way as to be "irreversible".
Prof Dame Angela McLean, deputy chief scientific adviser, earlier told the Commons science and technology committee that each step of easing measures should be "irrevocable", adding "that means we have to be extremely careful, before we add another unlocking".
"We want to understand the impact on each step before taking the next steps," she said, adding that required a "large gap" after children go back to school.
Prof Mark Woolhouse, an expert in infectious diseases from Edinburgh University who advises the government, said it was right to be cautious.
But he said it must also be recognised the falling rates of infection seen during lockdown were more encouraging than many thought they would be.
He said schools were not a "significant driver of infection" and there had never been a surge in cases seen across western Europe after reopening schools - although the new UK variant, which is more contagious, needed to be considered.
Also speaking at the committee earlier was Prof Sir John Bell, Oxford University's regius professor of medicine, who said it was "not plausible" to expect people to comply with major curbs after they have received two doses of vaccine.
"It's better to plan for that than to assume you can hold back the water with a dam, because you won't be able to," he said.
Infection rates are coming down - more quickly than many thought they would given the new more contagious UK variant.
The vaccination programme is also going well, providing protection to the most vulnerable. And the arrival of spring should be expected to help keep rates low.
So why the caution? While most believe Covid will become seasonal, a bounce-back in the summer is not being ruled out.
And even if rates rebound only a little, there are still large numbers of vulnerable people. Nearly half of hospitalisations have been in the under-70s.
What is more, high levels of infection at a time when vaccines are being rolled out and immunity being built provides the perfect breeding ground for new variants. Mutation may be unavoidable in the long-term, but encouraging them at this point would, many experts believe, be foolish.
It means the government is likely to be more cautious than some would want - and indeed maybe need to be given the cost of lockdown. But the judgement being made is it's better to go slowly and surely rather than having to take any more steps back.
Meanwhile, healthy volunteers will be infected with coronavirus to test vaccines and treatments in the world's first "human challenge" study which will take place in the UK.
Boris Johnson says it is "absolutely right" to take a "data not dates" approach to leaving lockdown, stressing England will ease measures "cautiously".
The prime minister said he will set out "what we can" in a road map for easing restrictions on Monday.
"We want to be going one way from now on, based on the incredible vaccination rollout," he said.
It follows a call from scientists for a data-led approach to lifting measures.
Speaking at a mass vaccination centre in Cwmbran, south Wales, Mr Johnson said relaxation of measures would be done in "stages" and that the reopening of hospitality was one of the last things to return after the first lockdown.
"You have to remember from last year that we opened up hospitality fully as one of the last things that we did because there is obviously an extra risk of transmission from hospitality," he said.
Asked whether he agreed with a data-led approach, Mr Johnson said "I do think that's absolutely right" and said the relaxation of measures will be "based firmly on a cautious and prudent approach", in such a way as to be "irreversible".
Prof Dame Angela McLean, deputy chief scientific adviser, earlier told the Commons science and technology committee that each step of easing measures should be "irrevocable", adding "that means we have to be extremely careful, before we add another unlocking".
"We want to understand the impact on each step before taking the next steps," she said, adding that required a "large gap" after children go back to school.
Prof Mark Woolhouse, an expert in infectious diseases from Edinburgh University who advises the government, said it was right to be cautious.
But he said it must also be recognised the falling rates of infection seen during lockdown were more encouraging than many thought they would be.
He said schools were not a "significant driver of infection" and there had never been a surge in cases seen across western Europe after reopening schools - although the new UK variant, which is more contagious, needed to be considered.
Also speaking at the committee earlier was Prof Sir John Bell, Oxford University's regius professor of medicine, who said it was "not plausible" to expect people to comply with major curbs after they have received two doses of vaccine.
"It's better to plan for that than to assume you can hold back the water with a dam, because you won't be able to," he said.
Infection rates are coming down - more quickly than many thought they would given the new more contagious UK variant.
The vaccination programme is also going well, providing protection to the most vulnerable. And the arrival of spring should be expected to help keep rates low.
So why the caution? While most believe Covid will become seasonal, a bounce-back in the summer is not being ruled out.
And even if rates rebound only a little, there are still large numbers of vulnerable people. Nearly half of hospitalisations have been in the under-70s.
What is more, high levels of infection at a time when vaccines are being rolled out and immunity being built provides the perfect breeding ground for new variants. Mutation may be unavoidable in the long-term, but encouraging them at this point would, many experts believe, be foolish.
It means the government is likely to be more cautious than some would want - and indeed maybe need to be given the cost of lockdown. But the judgement being made is it's better to go slowly and surely rather than having to take any more steps back.
Meanwhile, healthy volunteers will be infected with coronavirus to test vaccines and treatments in the world's first "human challenge" study which will take place in the UK.
