In a statement, Johnson savaged May's strategy, accusing her of allowing an optimistic Brexit vision to become clouded by a failure of ambition.
The Brexit "dream is dying, suffocated by needless self-doubt", he said in the letter, which he posted to Twitter.
She also said that the government had no intention of extending Article 50, which is a notice of intention to leave the European Union, and that there will not be a second national vote on this Brexit deal.
But she wakes up this morning facing the toughest challenge of her time in Downing Street to date.
Mrs May insists her plans are the "the best way to honour" the Brexit vote, amid a deepening political crisis.
While welcoming the UK's possible agreement to give the EU's top court a final say in the interpretation of union law when applied in the United Kingdom, they were quick to point out that any participation in the single market with regards to goods can be ruled out. Davis slammed the agreement, which promotes a "soft exit" from the European Union versus a swift, clean break, as giving away "too much away, too easily" to E.U. negotiators.
Mr Davis said that his departure was not a prelude to him challenging the prime minister's position, but said it was "not for me to make other peoples' decisions" on whether to follow his lead and to leave the cabinet. His replacement will be announced shortly.
Who will be the next Prime Minister if Theresa May loses a confidence vote?
India can build on T20 success, Pandya says
England lost the T20 series 2-1 to India after going down by seven wickets at the County Ground on Sunday. India never really got away from us, but we struggled to take wickets (during the chase)", said Morgan.
I am proud to have served as Foreign Secretary in your Government.
Opposition politicians were quick to capitalize on May's troubles.
The prime minister has warned the Tory party it must unite or face the prospect of Jeremy Corbyn in power.
"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".
Johnson, another loud pro-Brexit voice within May's divided government, slammed May in a resignation letter, accusing her of flying "white flags" of surrender in negotiations with the EU.
But in reality, she will be at the mercy of her party.
The announcement came half an hour before the Prime Minister was due to address MPs on the Cabinet agreement reached at Chequers last week, and a few hours before a crucial appearance before the 1922 Committee of Conservative MPs which could decide her fate. Yet if Brexit is to mean anything, it must surely give Ministers and Parliament the chance to do things differently to protect the public.
The Prime Minister enduring a bruising battle today as the two Cabinet heavyweights resigned over Brexit. "If they can't, make way for those who can", May told MPs on Monday, adding that she would consult European Union leaders during the North Atlantic Treaty Organisation summit later this week.
The likelihood of a Conservative leadership contest now looms.