Under the agreement reached between the two countries, the European Banking Authority (EBA), which employs 159 people, would be relocated from London to Frankfurt, the German magazine WirtschaftsWoche reported on Thursday, citing anonymous EU sources.
The EBA is perhaps best known for conducting regular stress tests on the EU's financial sector, which became a vital focus following the collapse of large parts of the banking sector.
Frankfurt's candidacy to become the new home of the EBA was set out by German Chancellor Angela Merkel at the end of May.
The European Medicines Agency (EMA), meanwhile, would move to Lille in France, the magazine said.
The EMA is one of the EU's biggest institutions with more than 900 employees, who supervise and monitor medicines developed for use in the EU and coordinates with around 1,600 companies. The agency has an annual budget of more than 300 million euros.
Germany, which applied to host both the EBA and the EMA, is among the nations looking to profit from the UK's departure from the EU.
EU states earlier this week tussled over moving EBA and EMA after Brexit, as most of them have expressed interest in hosting them.
Germany and Ireland are among the states that have said they will apply to host both bodies, though diplomats say no country will get both.
A final decision is expected in October after the EU states vote, first on the medical, then on the banking authority.
rd/sri (Reuters, dpa, AP)