The agreement, which requires approval by the European Parliament and by national parliaments would be implemented in 2014 and sets up the European Central Bank as the regulator of up to 200 of the eurozone's largest banks.
Individual countries would regulate the smaller banks, The New York Times reported Thursday.
"Europe and the euro area are providing proof that they are able to meet the challenges they face," said French President Francois Hollande in a statement.
"Today is not only a new day for Greece, it is indeed a new day for Europe," said Greek Prime Minister Antonis Samaras, who had another reason to be pleased, as approval was granted for $65 billion in bailout relief for Athens.
"The sacrifices of the Greek people have not been in vain," Samaras said.
The regulatory accord "marks an important step towards a stable economic and monetary union, and toward further European integration," said ECB President Mario Draghi.
Leaders said the agreement would allow the ECB to stretch beyond the 100-200 bank target and claim jurisdiction over any bank in the eurozone, the Times said.
German Chancellor Angela Merkel said the critical issue was separation of regulatory responsibilities and setting monetary policy. "We succeeded in securing Germany's key demands," Merkel said in Berlin.
The distinction between oversight and monetary policy included a "clear separation," she said.