Prime Minister Theresa May's office said May accepted the resignation on Monday and will announce a replacement soon.
The resignation of the Minister of foreign Affairs of great Britain Boris Johnson may have a significant impact on the format process, the release of Albion from the EU (Brexit).
"We're two years on from the referendum and the party of government seems more divided than ever", the Labour MP said.
His departure came just hours after former Brexit Secretary David Davis quit, saying he could not back and deliver the Government's plan as he does not believe in.
Above a picture of her cabinet, including her new foreign secretary, Jeremy Hunt, and Brexit minister Dominic Raab, May tweeted: "Productive Cabinet meeting this morning - looking ahead to a busy week".
She held a meeting of her new Cabinet on Tuesday before attending a Western Balkans summit in London with other European leaders.
The long-awaited document proposes keeping Britain and the European Union in a free market for goods, with a more distant relationship for services.
"But we will do this in a way which will be a smooth and orderly Brexit, a Brexit that protects jobs, protects livelihoods and also meets our commitment to no hard border" between the U.K.'s Northern Ireland and European Union member Ireland, she said.
With less than nine months before Britain leaves and just over three before the European Union says it wants a deal, Mrs May has been forced to show her cards that she will commit the country to pursuing the closest possible trading ties with the EU.
May's personal authority was badly damaged after she called a snap election a year ago to strengthen her hand in Brexit talks but instead she lost her parliamentary majority, meaning she has to rely on a small Northern Irish party to govern.
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May insisted earlier Thursday that her plan was exactly what Britons had voted for in the 2016 referendum. Asked if he was planning to quit, environment Secretary Michael Gove said "absolutely not".
Some Conservative Party lawmakers warned they would not tolerate a betrayal of Brexit.
"Dreaming is good, probably for all of us, but we have to deal with the real world", he said.
Some 48 letters would be required to trigger a vote.
"Nor do we expect a leadership challenge".
Davis quit late Sunday saying he could not support May's plans for close trade and regulatory ties with the bloc after the United Kingdom leaves the European Union next year.
With less than nine months left until Britain is due to leave the bloc, May is sticking to her plan for a "business friendly" Brexit, facing down hardline Brexit supporters in her Conservative Party who are livid over her plans to negotiate a "free trade area for goods" with the EU. The EU says it will respond once it has seen the details.
Appearing on the BBC's The Andrew Marr sShow on Sunday, he said: "I'm a realist and one of the things about politics is you mustn't, you shouldn't, make the ideal the enemy of the good". He has criticized May over her response to terrorism and approach to Brexit, and infuriated many in Britain when he retweeted a far-right group.
He was more enthusiastic about Johnson, calling him "a friend of mine".
Andrew Bridgen, a Tory backbencher, told the BBC: "I'm very, very disappointed with the offer that we've seen coming out of Chequers. I get along with her very well, I have a very good relationship".