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.
In a resignation letter circulated by local reporters, Davis told May he has repeatedly disagreed with the government over the past year and that it is looking "less and less likely" that the government can deliver Brexit per voters' wishes. That is a prospect that now seems more likely.
The double resignation on Sunday has the potential to derail May's government and set in motion a chain of events that could lead to an attempt to oust her as prime minister.
"All 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 told the BBC.
They feel Britain should have a clean break from the bloc and be liberated to pursue new trade deals with other countries, as well as to make its own laws, free from European influence.
But much of the day-to-day negotiation falls to May's office. But some senior pro-Brexit ministers have backed May's plan.
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. "That has been their practice throughout the a year ago and I fear, in fact, if anything, this is just the start".
"I like Theresa May, I think she's a good prime minister", Davis said.
Spain coach Fernando Hierro steps down following World Cup elimination
Fernando Hierro has quit his role as sporting director of the Spanish FA following the round-of-16 exit at the World Cup . Fernando Hierro with Andres Iniesta after the last 16 rounds defeat by Russian Federation at the ongoing World Cup.
Davis was the front-runner in the 2005 Conservative Party leadership contest, but lost to David Cameron.
"On the one hand it is odd the pound is in a decent mood, given that the "soft" Brexit plan agreed at Chequers is arguably in doubt following Davis" disappearing act, ' Campbell continued.
The resignation is a blow to Mrs May as she seeks to win over Eurosceptic MPs to her proposed Brexit vision. Environment Secretary Michael Gove said Sunday that it did not contain everything he wanted but "I'm a realist". It seeks to keep the United Kingdom and the European Union in a free-trade zone for goods, and commits Britain to maintaining the same rules as the bloc for goods and agricultural products.
Theresa May faces the greatest threat to her leadership since the general election as she prepares to confront furious backbench MPs on Monday in a bid to convince them to rally behind her Brexit plans.
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.
May will have a key meeting with members of her Tory party to discuss her plan in Parliament on Monday. The government is trying to convince lawmakers to back the agreed stance, inviting them, including those from the opposition Labour Party, for briefings on the plan.
Conservative MP Peter Bone said Davis had "done the right thing", adding: "The PM's proposals for a Brexit in name only are not acceptable".
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