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.
Brexit minister Steve Baker and unpaid parliamentary aides Conor Burns and Chris Green also resigned.
"I have a very good relationship".
"I'd be interested to see the actual white paper because there may be some nuances in it which may make people feel a bit happier", she told Sky News.
Some euroskeptic lawmakers dream of replacing May with a staunch Brexiteer such as Johnson, a populist, polarizing figure who has never made a secret of his ambition to be prime minister.
10 Downing Street confirmed Hunt's appointment on Twitter, after he was seen visiting the Prime Minister's official residence earlier in the evening. He said: "From what she has said Brexit does not mean Brexit and what we will end up with is the very worst of both worlds - still in the European Union but with no vote".
"Any attempt by the European Union to whittle away at the current proposal would see a significant number of MPs conceding that no deal is better than a bad deal". He also said he will "step up the preparations for "no deal" in case the spirit of pragmatism and compromise that we have extended is not reciprocated". Inside, the paper's report says May finds herself in a "serious crisis" caused by her "inability" to manage an orderly Brexit.
May replaced Davis with Dominic Raab, a strong Brexit supporter.
Later, he told the BBC the United Kingdom was giving "too much away, too easily" in negotiations with the EU.
"This is the Brexit that is in our national interest".
But as Foreign Secretary in May's government, he was prone to gaffes and criticized for not being on top of his brief.
But in reality, she will be at the mercy of her party.
Jacob Rees-Mogg, who leads a bloc of Brexit-supporting Conservative MPs in Parliament, urged May to give up on the plan. "It is the Brexit that will deliver on the democratic decision of the British people", May told parliament.
If she refuses to change course, she could face a leadership challenge. However, should she survive such a challenge, Conservative Party rules prevent her opponents from making another try to unseat her for at least a year. Many Brexit campaigners in her Conservative Party say she has betrayed her promise to pursue a clean break with the EU.