Prime Minister Theresa May announced Hunt's new role in a tweet, adding that the queen had approved the change.
But there was growing speculation about Mr Johnson's plans on Monday after he failed to attend a meeting of the Government's Cobra emergencies committee as well as a summit of Western Balkan nations being held in London.
Taking charge of the Foreign Office, Hunt said he would be standing "four square" behind the Prime Minister "so that we can get through an agreement with the European Union based on what was agreed by the Cabinet last week at Chequers".
Rebuffing claims that her proposals make too many concessions to the EU, May said her "smooth and orderly Brexit" would leave Britain free to make its own laws and trade deals.
"We're a hugely important country in the world still and we should have been making much more of that". After Johnson's departure she said she was "sorry and a little surprised" at his decision after ministers appeared to back her proposals.
Rodolfo Rodriguez: Full Story of 92-Year-Old Assaulted In Texas
Rodriguez, who doesn't understand English, still has no idea why he was attacked, his grandson, Erik Mendoza, told KCBS . The Spanish description includes more information, saying that the man has lost vision in his right eye.
She said: "My concern is that the Chequers' proposal is an opening bid in negotiations and the European Union may well try to erode the position agreed by the cabinet".
"The Government have no doubt that this support will continue", it said. Culture secretary Matt Hancock has replaces Hunt as health secretary.
May, the leader of the Conservative party, believed she had secured a hard-won agreement with her deeply divided cabinet of ministers on Friday to keep the closest possible trading ties with the EU.
Solicitor General Robert Buckland said: "She talked about Corbyn, she talked about the alternative which is delivering the country to the sort of government that I don't think people have voted for and certainly any Conservative voter would be repelled by".
May replaced Davis by appointing Dominic Raab as the new Brexit Secretary.
Asked if May should remain in power, Trump said "that's up to the people".
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. "Mr Speaker, this is the right Brexit", she said to jeers from the opposition Labour Party.
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