Two senior sources confirmed Mr Davis's departure from the cabinet.
"In my view, this policy has got a number of weaknesses".
Davis' resignation was followed by that of Exiting the EU Minister Steve Baker.
"I think one of the things it will do is make people very conscious of any further concessions".
At each stage I have accepted collective responsibility because it is part of my task to find workable compromises, and because I considered it was still possible to deliver on the mandate of the referendum, and on our manifesto commitment to leave the Customs Union and the Single Market. He urged May to abandon her plans and take a tougher line with Brussels.
After the hours-long meeting at Chequers, May seemed to have persuaded the most vocal Brexit campaigners in the cabinet, including Davis, to back her plan to press for "a free trade area for goods" with the European Union and maintain close trade ties.
In a statement, No 10 thanked Mr Johnson for his work and said a replacement would be announced shortly.
Mr Davis, who was appointed Brexit Secretary in 2016, said: "The general direction of policy will leave us in at best a weak negotiating position, and possibly an inescapable one".
Jacob Rees-Mogg, a leading Brexit hardliner, told Sky News: "This is very important. If the Brexit Secretary can not support them they can not be very good proposals".
Opposition Labour leader Jeremy Corbyn said his departure showed May had not authority left and was "incapable of delivering Brexit".
It is unclear whether Brussels will accept this, after repeatedly warning Britain it can not "cherry-pick" bits of its single market. Davis and his deputy resigned in protest against the blueprint, which keeps the United Kingdom bound to European Union rules on goods and food after the divorce.
He was well acquainted with the Brussels beat: he was Europe minister between 1994 and 1997 as the European issue tore apart then Conservative prime minister John Major's government.
Conservative MP David Davis arrives at Downing Street on July 13, 2016 in London, England.
Davis also served as a reservist in the Special Air Service, the British army's elite special force unit.
He ran for the Conservative leadership in 2001 and came fourth, but was made party chairman.
If Davis and Baker are the only major losses from the government over her plan for "a business-friendly" Brexit that proposes "a free trade area for goods" with the European Union, then May will be much safer.
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.
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