The resignation comes just hours before May was due in parliament to explain her plan for Britain to adopt European Union rules on goods after Brexit, amid anger from MPs in her own party who want a cleaner break.
- His departure leaves May with a hard task to find a replacement who can win the confidence of the pro-Brexit faction in May's Conservative Party whilst delivering on a Brexit plan that outraged many of them.
There have been differences within the Conservative Party over how far the United Kingdom should prioritise the economy by compromising on issues such as leaving the remit of the European Court of Justice and ending free movement of people.
She will face them at a meeting of the party later on Monday.
"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.
Davis quit late Sunday, saying he could not support May's plan to maintain close trade and regulatory ties with the European Union, commonly known as a "soft Brexit", after the departure takes place next year.
Davis opposed the PM's plan approved at her country residence, Chequers, on Friday.
"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 added.
Eurosceptic MP Steve Baker has also resigned.
Davis, a sharp operator and a gut-instinct politician, was a Leave campaigner in the referendum. He was promoted to the Department for Exiting the European Union as a parliamentary under-secretary in June a year ago.
A Brexiteer hailed his resignation as a "principled and fearless decision".
Opposition Labour leader Jeremy Corbyn said his departure showed May had not authority left and was "incapable of delivering Brexit".
The official portrait of David Davis. "That's not a tenable position".
The move, while not completely surprising, throws doubt on to how secure the government's Brexit strategy is.
Jacob Rees-Mogg, the leader of a Conservative group of Brexit supporters, said Davis' resignation proved that their concerns were well-founded and signaled that he would not vote for May's plan if it came to a vote in parliament. "I'd have to do something I didn't believe in", he told the BBC.
But Davis had expressed his unease over a compromise plan right up until the eve of the meeting, writing a letter to May describing her proposal to ease trade and give Britain more freedom to set tariffs as "unworkable". Environment Secretary Michael Gove said Sunday that it did not contain everything he wanted but "I'm a realist".
Conservative MP and Remainer Anna Soubry did not refer directly to Mr Davis's resignation, but tweeted it was "not the time for egos, grandstanding and blind ideology".
He said he was anxious the government's negotiating approach would "lead to further demands for concessions" from Brussels.
The director-general of the CBI, Carolyn Fairbairn, said the resignation was "a blow", adding that business had welcomed the agreement of ministers on Friday. But some senior pro-Brexit ministers have backed May's plan. "Now the Brexiteers holding Mrs May hostage are falling out, there isn't a majority for any withdrawal treaty in Parliament". "You deserve the final say".
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.
In a letter responding to Davis' resignation, May said she was "sorry" he had chosen to resign and argued her proposal was "consistent with the mandate of the referendum".