In his resignation letter, Mr Davis said he could no longer be an "reluctant conscript" to the Prime Minister's strategy on leaving the EU.
He was followed out of government by Steve Baker, his Leave-supporting deputy in the Brexit department, in an unprecedented crisis that puts Mrs May's survival as Conservative leader at serious risk.
Mr Davis had failed to publicly back a compromise struck by the Prime Minister with her cabinet following a meeting at Chequers that would effectively seek to keep the UK in a customs union with the EU for goods, maintaining a 'common rulebook' with Brussels.
In his letter to the Prime Minister published just over an hour after news of his resignation broke, at twenty to midnight on Sunday, Mr Davis wrote: "In my view the inevitable consequence of the proposed policies will be to make the supposed control by parliament illusory rather than real.
"As I said at Cabinet, the “common rule book” policy hands control of large swathes of our economy to the EU and is certainly not returning control of our laws in any real sense.
"I am also unpersuaded that our negotiating approach will not just lead to further demands for concessions."
In her reply, Mrs May told him: "I do not agree with your characterisation of the policy we agreed at Cabinet on Friday."
Foreign Secretary Boris Johnson backed the proposals at Chequers, despite claiming that defending the plans was like "polishing a turd" during the meeting.
Mrs May is scheduled to go before the 1922 Committee of Conservative backbenchers on Monday evening, after giving a statement to MPs in the Commons on the Cabinet agreement.
• READ MORE: In Full: David Davis’s resignation letter to the PM
With several Conservative MPs taking to social media to praise Mr Davis' announcement, it is unclear whether the Prime Minister's Brexit plan can command the support of her own party, or if she can avoid a leadership challenged triggered if 48 members of her parliamentary party send letters of no confidence to the chairman of the 1922 Committee.
efore Mr Davis' announcement, speculation had already been growing about a possible leadership challenge to the Prime Minister, with several Brexiteer Tory MPs rejecting the compromise and saying they would vote against it in parliament.
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.
Writing in The Daily Telegraph on Monday, Mr Rees-Mogg said: "If the proposals are as they currently appear, I will vote against them and others may well do the same."
A letter reported to be circulating among Tory MPs on Sunday is said to accuse her of "complete capitulation" and making promises that were "a pretence and a charade intended to dupe the electorate".
It is reported to conclude: "In the interests of our country and the future of Conservative Party, I feel the time has come for a new leader."
SNP Westminster leader Ian Blackford tweeted: "Theresa May will have an opportunity to choose her government's path. I call on the Prime Minister to see sense and bring forward a plan that heeds the mounting evidence against a hard Brexit from opposition parties, the business community and the devolved administrations.
He continued: "The question now for Theresa May is whether or not she fall in line to the demands of her party's extreme Brexiteers, or instead recognise the clear majority in parliament for the urgent need to keep the UK in the single market and customs union, to protect jobs and the economy."
Labour Party chairman Ian Lavery said: "This is absolute chaos and Theresa May has no authority left.
"The Prime Minister is in office but not in power. She cannot deliver Brexit and our country is at a complete standstill, while the Tories indulge in their leadership tussling.
"We can't go on like this. Britain needs a functioning government."