Prime Minister Theresa May announced Hunt's new role in a tweet, adding that the queen had approved the change.
A Downing Street spokesman said: "This afternoon, the Prime Minister accepted the resignation of Boris Johnson as Foreign Secretary".
Boris Johnson has resigned from his position as Foreign Secretary complaining Theresa May had "suffocated" the dream of Brexit.
Johnson reportedly was more blunt, describing the plan as a "turd".
In her statement to Parliament, May attempted to give an impression of business as usual, saying she would present a detailed paper onThursday on the government's negotiating position for a post-Brexit relationship with the EU. He built a public profile on Latin quips and rumpled eccentricity, while nurturing a poorly concealed ambition to lead his country.
Explaining his decision, Mr Davis said the United Kingdom was giving "too much away, too easily" in the Brexit talks, adding: "In my view, this policy has got a number of weaknesses".
She told her critics the alternative to the party coming together could be a left wing Labour administration, with Jeremy Corbyn as prime minister. 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.
The BBC's political editor Laura Kuenssberg said there were potentially "dozens" of Tory rebel MPs opposed to Mrs May's Chequers compromise.
Davis's late-night resignation undermines May's fragile government. European Union officials have warned Britain repeatedly that time is running out to seal a deal spelling out the terms of the divorce and a post-split relationship. The timetable looks increasingly optimistic.
Lawmakers howled as a beleaguered May paid tribute to two senior members of her Cabinet who resigned rather than accept her proposals.
The official portrait of David Davis.
Johnson, who favours a stronger break with the European Union, said in his resignation letter that Britain is "truly headed for the status of [EU] colony".
As the minister responsible for the Brexit negotiations, Mr Davis was a key voice in the debate in the UK.
May's government was rocked Monday by the resignations of Johnson and Brexit Secretary David Davis.
"I'd have to deliver this".
"However, even in that event it seems to me that the national interest requires a Secretary of State in my Department that is an enthusiastic believer in your approach, and not merely a reluctant conscript". "Others don't have that same responsibility".
The likelihood of a Conservative leadership contest now looms.