9 July 2018 08:55 pm
He is the second senior cabinet minister to quit within hours following Brexit Secretary David Davis's exit.
His departure came shortly before Theresa May began addressing Parliament about her new Brexit plan, which has angered many Conservative MPs.
She said she did not agree with the two ex-ministers about "the best way to honour" the result of the 2016 vote.
The BBC's political editor Laura Kuenssberg said Mr Johnson's exit had turned an "embarrassing and difficult situation for the PM into potentially a full-blown crisis".
She said he was not any ordinary cabinet minister but was the "face" of the Leave campaign during the 2016 referendum and his departure would fuel speculation about a leadership challenge.
She said she had been told by a source that either Theresa May "dumps" the plan signed off at Chequers or "another minister will go, then another, then another and then another".
The UK is due to leave the European Union on 29 March 2019, but the two sides have yet to agree how trade will work between the UK and the EU afterwards.
Theresa May only has a majority in Parliament with the support of the 10 MPs from Northern Ireland's Democratic Unionist Party, so any split raises questions about whether her plan could survive a Commons vote. There have also been renewed questions about whether she will face a challenge to her position.
Speaking in the House of Commons, Mrs May paid tribute to Mr Johnson's "passion" in championing a global Britain after Brexit and Mr Davis' work in steering through key Brexit legislation.
But she told MPs: "We do not agree on the best way to deliver our shared commitments to honour the result of the referendum."
PM May warned that if the EU did not engage with her plan, there was a "serious risk" of the UK leaving in March 2019 without a deal in a "disorderly" manner.