Europe's leaders hope that the deal will patch up a split that has held back the progress of the union. Greece's international lenders agreed on a package of measures to reduce Greek debt by €40bn, cutting it to 124pc of gross domestic product by 2020.
The move paves the way for releasing the next tranche of bailout loans -- which amounts to some €44bn.
The European Union's commissioner for economic and monetary affairs, Olli Rehn, praised Greece for keeping its commitments and said that the agreement was possible because "Greece has shown that it is serious about reform".
It was the eurozone's third meeting in two weeks on Greece.
European Central Bank chief Mario Draghi welcomed the decisions taken by the ministers of finance.
The decisions "will reduce the uncertainty and strengthen confidence in Europe and in Greece", Mr Draghi said.
Ministers committed themselves to take further steps to lower Greece's debt to "significantly below 110pc" in 2022.
This is the most explicit recognition so far that some write-off of loans may be necessary from 2016, the point when Greece is forecast to reach a primary budget surplus.