Davis was the front-runner in the 2005 Conservative Party leadership contest, but lost out to David Cameron, shedding momentum after a party conference speech fell flat.
"The general direction of policy will leave us in at best a weak negotiating position and possible an inescapable one", he wrote, adding: "The inevitable outcome of the proposed policies will be to make the supposed control by Parliament illusory rather than real".
"Outside of the EU, Britain will be nimbler, more open to innovation and technological change, at the same time as driving up global standards", he wrote.
Yet after reflecting on the situation, Mr Davis and Mr Baker apparently decided they could not live with such a soft Brexit after all.
Davis argued that this type of "soft Brexit approach" would leave the United Kingdom parliament in "at best a weak negotiating position".
In her reply, Mrs May told him: "I do not agree with your characterisation of the policy we agreed on at Cabinet on Friday".
After many months of rumours that he would pull the plug, David Davis has actually quit as Brexit Secretary. At the summit there were reportedly taxi business cards left in the foyer for ministers who, if they disagreed, would have to either get a taxi or walk home.
In a blow to the beleaguered prime minister, Davis told May in a letter that the government's proposals for close trade and customs ties "will leave us in at best a weak negotiating position, and possibly an inescapable one".
On Monday, May is due to brief lawmakers on the plan agreed by the Cabinet during its 12-hour meeting. Some lawmakers have already expressed their misgivings.
Since Friday, several more Conservative MPs were said to have added their names to a list supporting a vote of no confidence, although No 10 insiders have indicated May would fight any challenge and the numbers looked to be in her favour.
Asked if the prime minister could survive. Simply, if the Prime Minister can not unite her Cabinet and convince them over the Brexit negotiations, she has no chance of getting the European Union to agree to the terms. But pro-Brexit Conservative MPs called the proposal the "worst of all worlds".
"While I have been grateful to you for the opportunity to serve, it is with great regret that I tender my resignation from the Cabinet with immediate effect".
Mr Davis's resignation will anger cabinet colleagues from both wings of the party.
"We achieved all of the things that we campaigned for in order to ensure we could leave the European Union, but we also do so in a way which respects some of the wishes and some of the concerns of some of my colleagues that voted remain". Remainers will be angry that the apparent agreement that came from Chequers has been trashed, while Leavers who had to swallow their own opposition to the proposal will feel betrayed.
May's office said a replacement for Davis would be announced Monday.
On the worldwide markets, sterling slipped by a third of a cent against the dollar to $1.3288 in early trading.