In a joint statement afterwards, they said the deal was expected to unlock improvements in cross-Channel ties on trade, energy and security.
“They looked forward to the signing of Memoranda of Understanding on financial services and on intellectual property soon,” the read-out said.
The agreement will bring banking cooperation out of a deep freeze and is seen as the first step towards a wider deal with the EU for the City.
It will set up a new joint forum where senior figures from the two sides will meet regularly to discuss upcoming regulation and challenges in the sector.
Industry figures hope that, over time, it will improve trust levels to the extent that Brussels will drop its refusal to grant market access, known as equivalence.
Miles Celic, chief executive of TheCityUK, said: “This will be a vital step towards ensuring continued industry cooperation and continuity between the UK and EU.”