Davis was the front-runner in the 2005 Conservative Party leadership contest, but lost out to David Cameron, shedding momentum after a party conference speech fell flat.
Mr Davis's late-night resignation undermines Ms May's fragile Government.
But the Press Association understands that Mr Davis, who signed up to the plan agreed by the Cabinet at Chequers on Friday, has now quit.
While May's plan for exiting the European Union has not been fully revealed to all members of her party - let alone to Parliament, the business community or the public - the brief outline that was released shows she supports a middle way of compromise with Brussels, keeping Britain closely aligned with Europe on standards, "a common rule book for industrial goods and agricultural products". But pro-Brexit Conservative MPs called the proposal the "worst of all worlds".
The loss of her chief negotiator is a blow to the prime minister and comes as she prepares to face the House of Commons and then Tory MPs and peers on Monday to discuss her Brexit plans.
In that meeting, May had appeared to win over her fractious cabinet and secure approval for her plan, which was to be published as soon as this week in a lengthy white paper that would stake out Britain's vision for future relations with Europe.
In his resignation letter, he blamed the "dilution" of what he said was a firm Chequers agreement, delays to the White Paper, and omissions from the "backstop" customs proposal that would leave the United Kingdom in a "weak negotiating position at best".
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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.
Other Brexit-supporting Conservative lawmakers have criticised the Chequers "peace deal", saying that May's plans offered a Brexit in name only, a betrayal of what they saw as her promise for a clean break with the EU.
He said he was "unpersuaded" that the government's negotiating approach "will not just lead to further demands for concessions" from Brussels.
- To trigger a formal leadership challenge, 48 Conservative lawmakers need to write to the chairman of a committee which represents the interests of Conservative members of parliament who are not part of the government.
Speculation is mounting that others, including Foreign Secretary Boris Johnson, are ready to quit.
Johnson has not commented publicly since Friday.
The environment secretary, a leading Brexiter, said the deal the prime minister achieved at Chequers was not everything he had hoped for but insisted the cabinet was behind it and collective responsibility would prevail.
However, some of the party's most senior figures privately backed Remain in the referendum and it is acutely aware of how destabilising the process of leaving the EU has been for the Union. Past year reports emerged that Davis said he meant to "retire" in 2019 and leave the transitional period of Britain's exit from the European Union to Boris Johnson, something later dismissed as a "lighthearted remark".