
Prime Minister Theresa May announced Hunt's new role in a tweet, adding that the queen had approved the change.
Like Mr Gove - who infamously made a rival bid for the leadership after the referendum - Mr Johnson has always been suspected of aiming to lead the party and be prime minister.
Health Secretary Jeremy Hunt has been named as Mr Johnson's replacement as foreign secretary.
Specifically, she wanted to address the resignations of Johnson and Davis. "That dream is dying, suffocated by needless self-doubt", he wrote. "This mess is all of the Prime Ministers own making", opposition Labour Party leader Jeremy Corbyn told lawmakers.
Johnson had previously served as mayor of London and a lawmaker.
Why did David Davis resign?
Johnson quit on Monday over May's plan for Brexit, which includes a free-trade area for goods but little detail on the approach to services.
He claims crucial decisions have been postponed, including preparations for a "no-deal" scenario, "with the result that we appear to be heading for a semi-Brexit, with large parts of the economy still locked in the European Union system, but with no United Kingdom control over that system".
British Prime Minister Theresa May won support from many of her ministers, including a leading eurosceptic, on Tuesday after two top cabinet members quit saying her Brexit plan was too half-hearted.
Only three days ago, May appeared to have agreed on a deal with her fractured Cabinet on the UK's post-Brexit relationship with the EU.
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European Union officials say they will respond to the proposals once they have seen details.
This is the first time Mr Barnier has spoken about his lost negotating partner since the resignation, which triggered a huge Cabinet reshuffle after Boris Johnson followed shortly behind.
Less than nine months remain until Britain reduces the EU's membership on March 29, 2019. He also warned that Britain was "headed for the status of a colony" within the bloc.
The Sun, Britain's biggest-selling newspaper, said there had been "blunder after blunder" by May. "These two key cabinet resignations now increase the likelihood of a softer Brexit, an idea and concept that has always resonated well with sterling", says Hamish Muress, a currency analyst at OFX.
In her Commons statement, May urged the European Union to take her proposal seriously.
The spate of resignations has left May open to a leadership challenge from within her party that could topple the government and force an early election. "It requires them to think again and look beyond the positions they have taken so far and agree a fair balance of rights and obligations". Many see him as a future leader of the Conservatives and as a prominent Leaver he could stop the rush to topple the prime minister from the Brexit wing of the party.
Hours later UK Foreign Minister Boris Johnson resigned over the political crisis.
"I'd have to deliver this".
She told Sky News: "I'm happy to hear it will be published on Thursday".