“It is with great regret that we see our British friends leave the European Union,” Ms. Lagarde, president of the European Central Bank, said in a statement. “We will work hard to ensure Brexit causes as little disruption as possible for the citizens, employers and financial markets in the euro area and the rest of the E.U.”

The European Central Bank and the Bank of England have already set up a system to swap pounds and euros to ensure that banks don’t run short of either currency. Bank regulators on both sides have agreed to continue sharing information. And the European Central Bank has already issued licenses for 25 banks relocating from Britain to the euro currency zone.

Britain was never a member of the eurozone. But as a member of the European Union it contributed about 58 million euros, or $64 million, to the European Central Bank’s capital. It will now get that money back.

But fears that Brexit could hurt the European economy may already be proving justified. The eurozone grew only 0.1 percent during the last three months of 2019 compared with the previous quarter, according to official statistics published on Friday.

That was a significant slowdown from previous quarters and meant that the 19 countries in the eurozone grew only 1.2 percent during last year, according to a preliminary estimate.

“The specter of recession is back,” Christoph Weil, an economist at Commerzbank in Frankfurt, said in a note to investors on Friday.

Eurostat, the official statistics agency, didn’t give a reason for the slowdown. But one factor was probably the uncertainty caused by Brexit, which has made businesses hesitant to hire or to invest in expansion. Trade between the European Union and Britain has also shrunk since the country voted to leave.