The resignations came just days after May announced Friday that she had finally united her quarrelsome government behind a plan for a divorce deal with the EU.
Jeremy Hunt, who has been health secretary for the past six years, was a Remain campaigner in the 2016 European Union referendum.
He went on to explain how the current political turmoil in Britain will work to the EU's advantage in Brexit negotiations.
Less than nine months remain until Britain leaves the bloc on March 29, 2019, and the European Union has warned Britain repeatedly that time is running out to seal a divorce deal.
In his resignation letter, he said the Brexit "dream is dying, suffocated by needless self-doubt".
Cabinet crisis: Boris Johnson's resignation letter in full
The Guardian says the PM has faced down Brexit rebels "for now", reporting May's warning that divided cabinets lose elections. But as Foreign Secretary in May's government, he was prone to gaffes and criticized for not being on top of his brief.
"Perhaps, one side effect of my departure might be to put a little pressure on the government not to make any other concessions and I will keep arguing to say there is a better way to do it than this", Davis said.
Johnson said in his letter that May's plan to keep close economic ties with the bloc means Britain is heading for a "semi Brexit" that would leave Britain with the "status of a colony" of the EU. No 10 backed her last week when she was forced to apologise to the House of Commons...
Johnson rocked the Government by becoming the second Cabinet minister to resign in less than 24 hours.
Labour leader Jeremy Corbyn said Mr Johnson and Mr Davis had abandoned a "sinking ship", shattering the "illusion of unity" initially surrounding the Chequers plan.
May's office said in a terse statement that the prime minister had accepted Johnson's resignation and would name a replacement soon.
Matt Hancock replaced Hunt as health secretary, while Attorney General Jeremy Wright was appointed as minister of digital culture, media and sport, Hancock's old job.
"I'd have to deliver this".