Conservative MP Peter Bone hailed Mr Davis' resignation as a "principled and fearless decision", adding: "The PM's proposals for a Brexit in name only are not acceptable".
David Davis had already expressed unease over the compromise plan. A Brexiteer hailed his resignation as a "principled and courageous decision", BBC News reported.
Conservative MP Peter Bone said Davis had "done the right thing", adding: "The PM's proposals for a Brexit in name only are not acceptable".
Ian Lavery, chair of the Labour Party, said: "This is absolute chaos and Theresa May has no authority left".
If Davis" resignation emboldens the faction in favour of a "hard Brexit', she may end up facing a rebellion that could ultimately block her final exit deal when it is put before parliament in a vote expected later this year.
Google Duplex AI Assistant ready to replace call centers
The idea of calling a customer service rep and not knowing whether you're talking to a robot or a human is a bit unsettling. The company this afternoon denied The Information's report on "very early stage" testing of Duplex for call centers.
"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 effect of the proposed policies will be to make the supposed control by Parliament illusory rather than real".
His unhappiness in government has been no secret for some time, but after the prime minister's Chequers agreement with cabinet ministers to pursue closer ties with the European Union than he desired, he found his position untenable.
On Friday, May 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.
Brexit ministers Steve Baker and Suella Bravermanhas have also resigned.
On Monday, May is due to brief lawmakers on the plan agreed by the Cabinet during its 12-hour meeting.
Laura Kuenssberg, the BBC's political editor, tweeted that a former cabinet colleague of Mr Davis had said "it's a personal outburst. he's always struggled to muscle into any of the complicated arguments. he is a puff of smoke who will blow away like a dandelion".
Hospital Evacuated After Tuberculosis Sample Accidentally Released
King explained that the sample of tuberculosis consisted of only a few drops and did not pose a risk to those involved. Both cancer research buildings were evacuated out of an "abundance of caution" but have now been cleared as safe.
Some 34 per cent thought she should keep hold of the reigns, 24 per cent said she should resign now, while 24 per cent said she should step down after Britain formally leaves the European Union in March next year.
But in a sign of the trouble to come, Jacob Rees-Mogg, chairman of the European Research Group of Tory lawmakers, said May's plan was "defeatist" and he would oppose it.
The North Belfast MP said the DUP's "top priority" was protecting the Union but that on Brexit the government had to deliver "control of our borders, our laws and our money" while still retaining "sensible relationships" with EU countries.
As the minister responsible for the Brexit negotiations, Davis is a major voice in the debate in the UK.
Boris Johnson, a leading critic of the plans, spent several minutes at the Chequers summit spelling out his concerns, saying anybody defending the deal would be "polishing a turd" if they tried then to sell it to the party and the public.
Allies made it clear that the foreign secretary has not chosen to publicly support the Chequers deal yet - unlike Environment Secretary Michael Gove, Commons Leader Andrea Leadsom, and Trade Secretary Liam Fox.
Heatwave in Canada kills 33 people in a week as temperatures rise
Environment Canada expected temperatures to cool on Friday with much less extreme highs of 23C to 25C over the weekend. Twenty-eight of the deaths were in Montreal, said Marie-Claude Lacasse with the Ministry of Health.