But her spokesman signaled on Monday she would not back down over the "business friendly" agreement, saying May would now focus on moving the Brexit negotiations forward - a step European Union officials and businesses have long called for.
As the new secretary of state for exiting the European Union, Raab will now be in charge of leading negotiations for Britain's withdrawal from the EU. "An agreement was reached by the cabinet on Friday and now we are moving forward to negotiate that plan", the spokesman told reporters.
Davis's late-night resignation undermines May's fragile government.
In a move that unnerved Conservative Party eurosceptics, Steve Baker, a minister who worked for Davis, also quit, saying in his letter to May: "I can not support this policy with the sincerity and resolve which will be necessary".
In a letter responding to Davis' resignation, she said she was "sorry" he had chosen to resign and argued her proposal was "consistent with the mandate of the referendum".
On Friday, Davis and the rest of May's fractious Cabinet finally agreed on a plan for future trade ties with the EU.
Sterling rose, as traders bet Davis's resignation would not imperil May and instead focused on the newly-announced deal that markets believe makes a "soft Brexit" more likely. Davis and Baker, both longstanding eurosceptics, decided they could not support the policy, a person familiar with the matter said.
Conservative MP Marcus Fysh on Monday also refused to give his support to the prime minister, describing the government's policy as a "stinker" and warning: "If Theresa May wants to break her manifesto pledges that is up to her [but] these things have consequences".
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Brexit-backing lawmakers have been angered by May's plans, saying they will keep Britain too close to the European Union and limit its ability to strike new trade deals.
Tory Brexiteers have voiced concern about the agreement, with the chairman of the campaign group "Leave Means Leave" accusing May of personally deceiving Brexit campaigners.
May won the backing of her Cabinet on Friday for a plan that would create a "U.K. -EU free trade area".
After Cameron resigned following defeat in the Brexit referendum, Davis was appointed back into government by May, Cameron's replacement. Environment Secretary Michael Gove said Sunday that it did not contain everything he wanted but "I'm a realist".
The resignations dealt yet another blow to the beleaguered leader, just two days after she announced she had finally united her quarrelsome government behind her plan for a divorce deal with the EU.
May will have a key meeting with members of her Tory party to discuss her plan in Parliament on Monday.
Conservative lawmaker Jacob Rees-Mogg, a leader of the party's "hard Brexit" faction, compared May's plan to an egg so softly boiled that it "isn't boiled at all".
Tory Andrew Bridgen said he could not support the proposals that came out of Chequers, describing them as a breach of the red lines and that he wouldn't support it "even if the European Union were paying us for it".