The European Commission and Britain's finance ministry said in a statement that they had asked their respective central banks to form "a technical working group on risk management in the period around 30 March 2019 in the area of financial services".
Britain is set to leave the EU on March 29, 2019.
The group will be headed up by ECB president Mario Draghi and BoE governor Mark Carney, while Commission and Treasury officials will act as observers.
The statement said the technical work was separate from ongoing negotiations on the conditions for Britain's withdrawal and the future economic relationship between Britain and the bloc.
TheCityUK, a lobby group, welcomed the announcement as "a significant and welcome step in ensuring that financial services firms can continue to meet the needs of their customers".
"It is positive to see the European Commission and the UK Government taking a pragmatic and prudent approach," it said, adding that legal certainty on issues such as contractual continuity and access to data would be particularly important.
Businesses have complained of persistent uncertainty on both the terms of Britain's departure with less than a year to go and the conditions for a post-Brexit transition period due to end in 2020.