May's office said a replacement for Davis would be announced Monday.
Davis's departure was hailed by pro-Brexit Conservative lawmakers, who have long considered May too prone to compromise with the EU.
Mr Davis quit late on Sunday night, saying Theresa May had "given away too much too easily".
The immediate danger for May appeared to recede as pro-Brexit lawmakers held back from calling for her to go, emphasizing instead the need for a new policy. There was no immediate comment from Baker.
Davis' departure comes just nine months before Britain is scheduled to leave the European Union and 15 weeks before a final deal is to be signed.
After the Chequers summit, it emerged that Johnson had referred to attempts to sell the prime minister's Brexit plan as "polishing a turd". It vows to press for a free trade area for goods with the European Union and maintain close links.
Brexit-backing MPs have been angered by Ms May's plans, saying they will keep Britain too close to the European Union and limit its ability to strike new trade deals.More news: US economy adds more jobs than expected in June
"As I said at Cabinet, the "common rule book" policy hands control of large swathes of our economy to the European Union and is certainly not returning control of our laws in any real sense".
"I think one of the things it will do is make people very conscious of any further concessions".
"It seems to me that the national interest requires a secretary of state in my department that is an enthusiastic believer in your approach, and not merely a reluctant conscript", he wrote.
"I do not agree with your characterisation of the policy we agreed", she said, asserting that it "will undoubtedly mean the returning of powers from Brussels to the United Kingdom". But some senior pro-Brexit ministers have backed May's plan.
Jacob Rees-Mogg, who commands about 60 hardline euroskeptics, said a confidence vote wasn't in the offing and said he thought May would still be premier in March, when Britain is due to leave the bloc.
"A wider rebellion, a leadership challenge, early elections and possibly another major shift in the Brexit strategy (either way) can not be ruled out", Citi said in a note to clients. Michael Gove, May's environment minister, said on Sunday that while the agreed negotiating stance was not ideal, he believed it delivered on handing back control to Britain.
Boris Johnson has resigned as Foreign Secretary amid a growing political crisis over the UK's Brexit strategy.
He told BBC 5 Live: "These proposals will have to come to the House of Commons in legislation and the question is 'will they command support from Conservative MPs?'".