Britain's Secretary of State for Departing the EU David Davis arrives in Downing Street in London, June 26, 2018.
Davis has been locked in bitter disputes with the Prime Minister and her chief Brexit adviser Olly Robbins for months.
In a statement, No 10 thanked Mr Johnson for his work and said a replacement would be announced shortly.
Davis said the so-called "soft Brexit" plan, which proposes maintaining a "UK-EU free-trade area" would leave the U.K.in "at best, a weak negotiating position and at worst, an inescapable one".
Davis was appointed two years ago to head up the newly created Department for Exiting the European Union after Britain voted to leave the bloc in a referendum.
But much of the day-to-day negotiation falls to May's office.
Jacob Rees-Mogg, a key figure in the Conservative Party's "hard Brexit" faction, which supports relinquishing access to the EU's single market in exchange for full border control, said the deal would be "worse" than a United Kingdom exit from the European Union with no deal at all. "That has been their practice throughout the past year and I fear, in fact, if anything, this is just the start".
In a letter to May, Davis said he was not willing to be "a reluctant conscript" to her negotiating stance.
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The hurricane center cautioned those along the coast to keep an eye on Chris but think its worst weather will stay offshore. Forecasters are also tracking Beryl , which weakened from a Category 1 hurricane to a tropical storm over the weekend.
Davis' resignation was followed by that of Exiting the EU Minister Steve Baker.
May is due to address parliament on Monday to explain her plan for Britain to adopt European Union rules on goods after Brexit, amid anger from MPs in her own party who want a cleaner break and businesses who say it may still cause economic harm.
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. Trade Secretary Liam Fox put his name to a newspaper article backing May's plan, and Environment Secretary Michael Gove defended it in a TV interview.
But Davis had expressed his unease over a compromise plan right up until the eve of the meeting, writing a letter to May describing her proposal to ease trade and give Britain more freedom to set tariffs as "unworkable". They have criticised the Chequers deal as offering a soft Brexit that betrays what they believe was a mandate for a clean break with the EU.
The resignation of Davis on Sunday evening has dealt a major blow to May, who has struggled to unite factions within her ruling Conservative Party.
On Friday night she appeared to have persuaded hardline Brexiteers in the Cabinet, including Davis, to back her plan.
He told BBC 5 Live: "These proposals will have to come to the House of Commons in legislation and the question is 'will they command support from Conservative MPs?'". If May fails to stabilise her party tonight then there is, for the first time, a real risk that Tory MPs will decide that enough is enough.