Speaking tonight, Mr Hunt said he would be supporting Mrs May in her efforts to secure a Brexit deal with Brussels.
The resignations are a stunning reversal from Friday's special Cabinet at Chequers when all ministers signed up and Johnson proposed a toast to the deal - even suggested a joint newspaper column with Chancellor Philip Hammond.
Johnson said that at a meeting of the cabinet to decide the plan on Friday, he had accepted that "my side of the argument were too few to prevail".
Davis and his deputy quit just two days after May announced she had finally united her quarrelsome government behind a plan for a divorce deal with the EU.
Former Health Secretary Jeremy Hunt leaves No. 10 Downing Street after accepting the position of foreign secretary following the resignation of Boris Johnson on July 9 in London.More news: Trump's scandal-hit environment chief Pruitt resigns
More news: Protesters confront McConnell leaving Kentucky restaurant
More news: DAMN YANKEES Star Tab Hunter Dies at 86
Late Monday, Hunt tweeted that it was a "h$3 uge honour to be appointed Foreign Secretary at this critical moment in our country's history".
But it soon began to unravel, when Davis resigned late on Sunday and launched a no-holds-barred attack on her plan, calling it "dangerous" and one which would give "too much away, too easily" to European Union negotiators, who would simply ask for more. "Since I can not in all conscience champion these proposals, I have sadly concluded that I must go". Uncertainty over whether tariffs and immigration checks would be introduced at the border has been a major stumbling block in negotiations between Britain and the European Union.
Rebuffing claims that her proposals make too many concessions to the EU, May said "this is the right Brexit" and would leave Britain free to make its own laws and trade deals.
As I said then, the Government now has a song to sing.
"I like Theresa May, I think she's a good prime minister", Davis said. The trouble is that I have practised the words over the weekend and find that they stick in the throat. Since I can not in all conscience champion these proposals, I have sadly concluded that I must go. As I leave office, the FCO now has the largest and by far the most effective diplomatic network of any country in Europe - a continent which we will never leave.