They agreed on Thursday night at the start of their two-day summit in Brussels to create the legal framework for the gigantic project by the end of this year and to begin its operation gradually next year.
Under the plan, more than 6,000 banks in the 17-nation euro zone will be put under the single supervisory body, which will be led by the European Central Bank based in Frankfurt.
Announcing the agreement at the end of the opening session, which lasted until the early Friday, President of the European Council Herman Van Rompuy said the Single Supervisory Mechanism, which aims to prevent banking risks and cross-border contagion, is an important step towards a stable economic and monetary union.
As soon as the SSM comes into force in 2013, it will open the way for the euro zone's permanent bailout fund, the European Stability Mechanism, to recapitalise the troubled banks directly, Rompuy said in a press statement.
The euro zone finance ministers will work out the modalities of the ESM injecting capital directly into banks, without adding to their governments' debts.
The ECB, which has a central role in the supervisory body, has been given powers to intervene directly in any euro zone banks, Rompuy said.
The EU leaders also agreed that the ECB's banking supervisory functions
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