May is holding a meeting of her new-look cabinet on Tuesday, following a forced reshuffle in the aftermath of the resignations.
10 Downing Street confirmed Hunt's appointment on Twitter, after he was seen visiting the Prime Minister's official residence earlier in the evening. Corbyn, addressing May in parliament, said her government should be ended if it was incapable of governing.
May acted quickly to replace the ministers.
"Jeremy Hunt MP as Secretary of State for Foreign and Commonwealth Affairs", Downing Street said in a statement. Inside, the paper's report says May finds herself in a "serious crisis" caused by her "inability" to manage an orderly Brexit.
Brexit-supporting lawmakers were angered by the proposals, saying they would keep Britain tethered to the bloc and unable to change its rules to strike new trade deals around the world.
Johnson's resignation was more perilous for May given his seniority in government. "The Prime Minister thanks Boris for his work".
"This is the Brexit that is in our national interest".
The decision by Johnson, a former mayor of London, to back Brexit, was seen as crucial when the issue was taken to a referendum two years ago.
Some Brexiteers think the most crucial issue is to ensure that Britain actually leaves the European Union in March next year, and feel that whatever arrangements Mrs May has secured can always be renegotiated once that point has been reached.
But as Foreign Secretary in May's government, he was prone to gaffes and criticized for not being on top of his brief.
There was no immediate statement from Mr Johnson to explain his decision to quit, which was seized upon by opposition politicians as a sign of increasing turmoil within Mrs May's administration. "Two secretaries of state have resigned and still we are no clearer as to what our future relationship with our nearest neighbors and biggest trading partners will be".
More crucially, Mr Johnson is wrong to say that the laws in question were "supported at every level of UK Government".
At a Cabinet meeting Friday, May demanded members support a plan for Brexit that it would include Britain partly remaining in the single market and signing up to a "common rulebook" for goods. "But there are people in Labour and the Liberal Democrats who wish to damage the sort of Brexit that many of my constituents have voted for".
Mairead McGuinness, vice president of the European Parliament, said the fact the white paper will still be published on Thursday "bodes well" for ploughing ahead with presenting the plan to the EU.