"Money will be flowing to Greece as early as next week," Eurogroup Chairman Juncker told a news conference after a meeting of ministers from the single currency bloc.
"We are convinced the programme is back on a sound track."
The decision, announced on Thursday (13 December) clears the way for an EU leaders' summit opening in Brussels on the same day.
A Eurogroup statement said €34.3 billion would be paid out in the coming days and the remainder in the first quarter of 2013.
"This has three elements," said Klaus Regling, the head of the eurozone's bailout funds, the ESFS and the ESM – "€16 billion for the bank recapitalisation and bank resolution, 7 billion for budgetary financing and 11.3 billion euro to finance the debt buyback."
Agreement to release the funds hinged on the success of a debt buyback launched by Greece last week, which will enable Athens to retire nearly €20 billion in bonds repurchased at a third of their face value from private holders.
Juncker said he was not sure that additional measures would be needed to reach an agreed goal to bring Greece's debt down to 124% of gross domestic product (GDP) by 2020, but the bloc stood ready to take new steps if necessary.
Christine Lagarde, IMF manging director, was more confident about Greece's ability to meet its debt reduction goals. "These steps will ensure that Greece's debt-to-GDP declines to 124% by 2020 and to substantially below 110% by 2022," she said.
