Two senior sources confirmed Mr Davis' departure from the Cabinet.
Mr Davis' decision could now act as a spur to other Brexiteers to take action against Mrs May.
Jacob Rees-Mogg, the leader of a group of Brexit supporters in the Conservative Party, said Davis' resignation proved that their concerns were well-founded.
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.
"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".
Britain's Secretary of State for Exiting the European Union David Davis leaves 10 Downing Street, London, January 29, 2018.
Heavy-hearted Murray pulls out of Wimbledon
Murray also wrote that he would start practicing on the hard courts right on Monday, with a view to a full return during the U.S. Kate, a lifelong tennis fan, often shows her support to Andy Murray and has even watched him play at the men's final.
Beryl becomes first hurricane of 2018's Atlantic hurricane season
Small storms can morph quickly - Beryl flared up from a depression Thursday morning to a hurricane in less than 24 hours. The Met Office assured the public that Trinidad and Tobago is not under any Tropical Storm watch or warning.
Six deaths in Montreal linked to heat wave
Mayor Valérie Plante urged people to check on vulnerable neighbours, including seniors. A NUMBER of people have died because of a heatwave in central and eastern Canada .
May was expected to tell MPs that the strategy agreed on at Chequers is the "right Brexit" for Britain.
Jenkyns said Steve Baker, a junior minister in the Brexit department, had also quit.
The Press Association news agency, the BBC and others say Brexit Secretary David Davis resigned Sunday, 48 hours after May announced that her divided government had at last agreed on a plan for ties with the European Union after the United Kingdom leaves next year.
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". The resignations further complicate that process, and put a question mark over whether she can get the backing of parliament for her Brexit plans and whether there may be a leadership contest.
Labour leader Jeremy Corbyn said Mrs May was "incapable of delivering Brexit". On Friday she achieved a rare consensus in a key cabinet meeting at her Chequers country house estate on the way forward for the negotiations with the EU. Environment Secretary Michael Gove said Sunday that it did not contain everything he wanted but "I'm a realist".
Britain's Prime Minister Theresa May and her cabinet discuss the government's Brexit plans at Chequers, the Prime Minister's official country residence, near Aylesbury, Britain.
Foreign Secretary Boris Johnson backed the proposals at Chequers, despite claiming that defending the plans was like "polishing a turd" during the meeting.
What appears to have kickstarted the resignations, however, is May's reintroduction of "collective responsibility", a British convention which means ministers are formally banned from disagreeing with government policy, including the Brexit plan.