The surprise announcement late on Sunday night follows tensions in the Cabinet over the prime minister's vision for the UK's post-Brexit relationship with the European Union, which has been heavily criticised by the pro-Brexit wing of her party.
Mr Davis and fellow Brexit backer foreign secretary Boris Johnson had both agreed to support Mrs May's proposal for a softer divorce than she had originally planned, and it seemed she had survived the storm.
"David Davis has done the right thing, a principled and fearless decision", he said. A Brexiteer hailed his resignation as a "principled and fearless decision", BBC News reported.
Mr Davis said the "current trend of policy and tactics" was making it look "less and less likely" that Brexit would deliver on the referendum result and the Tory commitments to leave the EU customs union and single market.
Conservative MP William Wragg, who campaigned for Brexit, said the resignation was "the right thing to do" while Tory MP Andrea Jenkyns, who quit a junior government role earlier this year to "fight for Brexit", said it was "fantastic news", adding: "Well done David Davis for having the principle and guts to resign".
"The general direction of policy will leave us in at best a weak negotiating position and possible an inescapable one", he wrote, adding: "The inevitable outcome of the proposed policies will be to make the supposed control by Parliament illusory rather than real".
The Sun newspaper's political editor Tom Newton-Dunn said on Twitter that it appeared that there was the possibility of a move against Mrs May as prime minister starting.
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Before his letter of resignation was made public, Davis's allies told the British press that he was resigning because he could not support the soft Brexit plan pushed forward by May at a crunch cabinet meeting Friday at the prime minister's countryside estate, called Chequers.
Another minister from the Brexit department, Suella Braverman, was also reported by local media to have resigned, although there was no official confirmation and she did not respond to a request for comment.
- Davis led Britain's negotiations in Brussels on the terms of the European Union divorce, and the future relationship with the bloc.
Mrs May will have a key meeting with members of her Tory party to discuss her plan in Parliament on Monday. 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.
Jacob Rees-Mogg, the chairman of the European Research Group of Brexiteer backbenchers, was openly touted as the only candidate who could deliver Brexit by one MP, Andrew Bridgen.
Trade Secretary Liam Fox put his name to a newspaper article backing the plan, and Environment Secretary Michael Gove defended the agreement in a TV interview.
However, Michel Barnier, the EU's chief Brexit negotiator, welcomed the plan and said: "I am ready to adapt our offer should the United Kingdom red lines change".