One other ministers in his department has also quit, with reports that another has done so.
The Prime Minister secured Cabinet backing for the strategy in a marathon meeting at Chequers last week, but has since faced a backlash from hardline Brexiteers - with some questioning her leadership. Parliament will decide whether or not to back the deal the government negotiates, but that deal will undoubtedly mean the returning of powers from Brussels to the United Kingdom.
"We achieved all of the things that we campaigned for in order to ensure we could leave the European Union, but we also do so in a way which respects some of the wishes and some of the concerns of some of my colleagues that voted remain".
The UK would of course continue to play a strong role in shaping the worldwide standards that underpin them, and Parliament would have oversight of the incorporation of these rules into the UK's legal order - with the ability to choose not to do so, recognizing that this would have consequences.
He criticised May's decision to maintain a "common rule book" with the European Union, mirroring the bloc's rules and regulations, saying it would hand "control of large swathes of our economy to the European Union and is certainly not returning control of our laws".
While Mays plan for exiting the European Union has not be 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".
Mr Davis had disagreed with the PM's plans for keeping European Union rules for goods and adopting a close customs partnership with the other 27 member countries.
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.
The EU's chief Brexit negotiator Michel Barnier said he was looking forward to the publication of the white paper and the EU would consider whether the proposals are "workable and realistic".
The prime minister's official spokesman said she would fight any attempt to oust her as prime minister if the required 48 Tory MPs called for a contest.
Boris Johnson was joking but his frustration was self-evident.
"Politicians come and go, but the problems they have created for their people remain", European Council President Donald Tusk said Monday of Daviss exit, just before being informed of Johnsons resignation.
Yet after reflecting on the situation, Mr Davis and Mr Baker apparently decided they could not live with such a soft Brexit after all.
Pro-European MPs who had previously rebelled against May also offered their support for the plan, with Anna Soubry saying it "delivers a business friendly Brexit". Some lawmakers have already expressed their misgivings.
Arch-Brexiteer Jacob Rees-Mogg hit out at the "defeatism" in the Government's plans, warning that he would vote against them - and suggested other Eurosceptics may do the same. My concern is that the PM's red lines got rubbed out. This would allow Britain to set its own import tariffs and seal new free trade deals.
Asked if she could survive, he replied: "oh yes, of course".
She paid tribute to Mr Johnson's "passion" in championing a global Britain after Brexit and Mr Davis' work in steering through key Brexit legislation. "It's more important to do what you have promised the British electorate than stick by lines in the sand".
British Prime Minister Theresa May and the Cabinet came to a general agreement on trade and customs issues after Brexit. "It was the right thing to do".
Peter Bone welcomed Mr Davis' resignation, saying it was "a principled and courageous decision". I take my hat off to you. She knew this because I had written to her earlier in the week."He admitted he had "lost the argument in Cabinet", adding: "In my view, this policy has got a number of weaknesses".
Two senior sources confirmed Mr Davis' departure from the Cabinet.