Mr Johnson, who led the campaign for Britain to leave the EU, will also meet with US Secretary of State John Kerry.
Ministers will discuss the Nice attacks and the defeated coup in Turkey but have stressed there will be no formal discussions about Britain's EU exit.
Mr Johnson's journey to the talks was delayed after his plane had to make an emergency landing.
The delay meant the newly-appointed Cabinet member was late for an informal dinner with EU foreign policy chief Federica Mogherini on Sunday evening.
James Robbins, the BBC's diplomatic correspondent, said although Brexit was not on the agenda "Mr Johnson's fellow ministers are bound to be sizing up their nemesis".
"Today's meetings are bound to be odd, when the man who compared the EU's ambitions to create a super-state to those of Adolf Hitler, sits down with the 27 other ministers," he added.
The meeting comes after new Brexit Secretary David Davis said EU migrants who come to the UK as a departure date nears may not be given the right to stay.
He said there might have to be a cut-off point if there was a "surge" in new arrivals but any steps must be compatible with EU law.