Some euroskeptic lawmakers dream of replacing May with a staunch Brexiteer, such as Foreign Secretary Boris Johnson, who in the past has disagreed publicly with his boss.
"I would like to thank you warmly for everything you have done over the past two years as Secretary of State to shape our departure from the European Union", she said.
Davis, who campaigned for Brexit in Britain's 2016 referendum, said he had resigned because the cabinet deal had given "too much away, too easily" to European Union negotiators, who, he feared, would simply ask for more.
Davis said it risked breaking campaign promises, would trigger more concessions, and could end up with Britain staying in the single market and customs union.
Asked whether Mr Raab was signed up in full to the plan agreed at Chequers, Mrs May's official spokesman told reporters: "The Government's position was agreed on Friday".
The junior Brexit minister, Steve Baker, also resigned, Downing Street confirmed Monday.
David Davis said he "wouldn't have done a good job" of delivering May's Brexit plan, with Tory MP Marcus Fysh saying the plan is paramount to breaking manifesto pledges, which "has consequences".
The 69-year-old had reportedly threatened to quit several times over a perceived lack of firmness in Britain's negotiating stance but had remained strictly loyal to the prime minister in public.
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"May's Brexit means BRINO - "Brexit In Name Only" - a fake Brexit", said John Longworth, co-chairman of Leave Means Leave.
Guy Verhofstadt, the European Parliament's chief Brexit coordinator, said he had enjoyed working with Davis and that he hoped Britain would unite "around a position to conclude a broad Association Agreement with the EU".
Denying that he wanted to unseat the prime minister, he said he would now "argue for being as firm as possible". 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.
The Tory leader's hard-won proposal was agreed to at her Chequers country retreat after marathon talks on Friday.
She will face them at a meeting of the party later on Monday.
So to criticise Friday's plan, ministers would have to resign and immediately give up ministerial staff, salary, and perks including government cars.
His resignation comes days after Theresa May secured the cabinet's backing for her Brexit plan despite claims from Brexiteers that it was too "soft".
He told the BBC a contest would take three months and "we physically do not have the time for that" given the United Kingdom is due to leave the European Union next March and both sides want a Brexit deal by October.