Prime Minister Theresa May's office said May accepted the resignation on Monday and will announce a replacement soon.
Davis resigned late Sunday, saying May's plan to maintain close trade and regulatory ties with the European Union gave "too much away, too easily".
Mrs May said she was "sorry - and a little surprised" by Mr Johnson's move after his apparent support on Friday.
"I think it is right that the cabinet backs the prime minister and speaks with one voice and if people don't do that then they have to go", Justice Secretary David Gauke told BBC radio.
Like Mr Gove - who infamously made a rival bid for the leadership after the referendum - Mr Johnson has always been suspected of aiming to lead the party and be prime minister.
The British public no longer has faith in Theresa May to negotiate Brexit, with two in three saying they do not trust her to get the best possible deal, a Sky Data poll reveals.
If Davis' resignation rattled May, Johnson's shook the foundations of her government.
She also said that the government had no intention of extending Article 50, which is a notice of intention to leave the European Union, and that there will not be a second national vote on this Brexit deal.
"I want to see more detail from the Chequers agreement, but I feel reassured that the main issues have been addressed and delivered, including free movement of people".
On Monday, minutes after Johnson quit, May defended her Brexit plan to lawmakers in the House of Commons - with Johnson absent from his usual place on the Conservative front bench.
"Over the coming days, weeks and months these negotiations will become more intense as we head towards leaving the European Union on March 29, 2019".
In her statement to Parliament, May attempted to give an impression of business as usual, saying she would present a detailed paper onThursday on the government's negotiating position for a post-Brexit relationship with the EU. "This mess is all of the Prime Ministers own making", opposition Labour Party leader Jeremy Corbyn told lawmakers. And she was given a reprieve tonight with news she will not face an immediate vote of no confidence.
"Friday's announcement was turning red lines into a white flag, and David Davis has made that so clear in his resignation letter", Rees-Mogg said.
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