"The general direction of policy will leave us in at best a weak negotiating position, and possibly an inescapable one", Davis said in a letter to May.
Davis and Baker, both longstanding euroskeptics, decided they couldn't support the policy, a person familiar with the matter said.
Mr Davis was responsible for negotiating the UK's European Union withdrawal.
William Wragg, another backbench Eurosceptic said: "I've reserved judgement on the Chequers' Brexit plan, but I have grave misgivings about it and understand entirely why David Davis has found it necessary to resign".
Serena Williams beats Mladenovic to give notice that comeback title is on
The 36-year-old American now can not meet a top 32 player until the semi-finals after the scattering of the seeds this week. Keys also came up short with a comeback attempt after fighting back from a set and two breaks down, losing 7-5, 5-7, 6-4.
Before his letter of resignation was made public, Davis's allies told the British press that he was resigning because he could not support the soft Brexit plan pushed forward by May at a crunch cabinet meeting Friday at the prime minister's countryside estate, called Chequers.
Davis, Baker and other pro-Brexit members of May's Conservative Party have deep concerns about her plans for keeping the United Kingdom tied to European Union rules for goods and adopting a close customs arrangement with the other 27-member countries.
The 100-page Brexit white paper, due this week, was the subject of a freakish ping pong between Dexeu and the Cabinet Office Europe unit, which repeatedly vetoed its language - and this was the reason for its delay, and the argument meant to be settled by Chequers.
"Those of us who believe that we want to execute a proper Brexit, and one that is the best deal for Britain, have an opportunity now to get behind the prime minister in order to negotiate that deal", he said. Some lawmakers have already expressed their misgivings.
"An egg which is very softly boiled isn't boiled at all; a very soft Brexit means we haven't left, we're simply a rule-taker", Rees-Mogg observed after May's plans were announced.
Wildfire forces evacuations near Warm Springs; U.S. 26 reopened
Highway 160 remains closed and officials said they could not estimate when it will reopen or when the evacuation orders will end. Monday it had burned approximately 42,000 acres - roughly 1,100 acres an hour since it was reported at 2:12 p.m.
Chief whip Julian Smith was inviting MPs to Downing Street to hear from the Prime Minister's chief of staff Gavin Barwell for a briefing on the Chequers proposals in a bid to win them round ahead of Monday's meeting.
Conservative MP Peter Bone said Mr Davis had "done the right thing", adding: "The PM's proposals for a Brexit in name only are not acceptable".
"Fantastic news", tweeted Andrea Jenkyns, a Conservative lawmaker. I take my hat off to you. But rats leaving a sinking ship is not enough, we need their captain to go, Theresa May's time is up. 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.
But Mr Davis's concerns stretched well beyond the actual policy that he would have been forced to sell in a tour of European capitals, starting this week.
On the global markets, sterling slipped by a third of a cent against the dollar to $1.3288 in early trading.
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CHRIS FROOME faces a fight to defend his Tour de France title after the race's organisers tried to ban him from the startline. A decision is set to be made the following day, with just three days to go until the start in the Vendee on July 7.