Davis was a strong pro-Brexit voice in a Cabinet divided between supporters of a clean break with the bloc and those who want to keep close ties with Britain's biggest trading partner. A new secretary would be announced on Monday, May's office said.
His comments came after Andrea Jenkyns, who recently quit a Government role to campaign for Brexit, said she would vote against any such deal, adding "if the detail is as bad as were hearing, then I'm also prepared to put a letter into the [1922 Committee]".
Mr Davis had come close to resigning before, but Mrs May must have hoped the danger of Cabinet resignations had passed after Friday's deal at her official country retreat. There was no immediate comment from Baker.
Less than nine months remain until Britain leaves the bloc on March 29, 2019.
The UK's David Davis has been confirmed to have resigned from his position as Brexit Secretary following the UK cabinet's agreement to PM May's new Brexit proposal, with hard-line Brexiteers including Davis angry over the agreement, claiming that the new proposals betray the original referendum result.
May will have a key meeting with members of her Tory party to discuss her plan in Parliament on Monday. "As I said at Cabinet, the "common rule book" policy hands control of large swathes of our economy to the European Union and is certainly not returning control of our laws in any real sense". "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".
Tiger Woods, Phil Mickelson reportedly planning $10 million match
A winner-take-all match will give the victor ultimate bragging rights for the rest of his life - not to mention $ 10 million . Alan Shipnuck reported that the event at one time was planned for Tuesday, the day before Independence Day, in Las Vegas .
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.
"A very soft Brexit means that we haven't left, we are simply a rule-taker", he said.
Jacob Rees-Mogg, chair of the European Research Group of Tory Europsceptic MPs was being urged to run for leader, with one even naming him as "our Churchill".
Some dream of replacing May with a staunch Brexiteer, such as Foreign Secretary Boris Johnson, who in the past has disagreed publicly with his boss. Their stand may embolden pro-Brexit lawmakers to make a move against her.