After Brussels talks, the ministers agreed to unlock 10.3 billion euros ($11.5 billion) in new loans.
The move came two days after the Greek parliament approved another round of spending cuts and tax increases demanded by international creditors.
The 19 eurozone ministers – known as the Eurogroup also said debt relief would be eventually offered to Greece.
This had been a key demand from the IMF, which says public debt is unsustainable at current levels of about 180% of Greece’s gross domestic product.
The deal was announced after 11 hours of talks between the Eurogroup ministers.
Eurogroup President Jeroen Dijsselbloem told reporters on May 25: “We achieved a major breakthrough on Greece which enables us to enter a new phase in the Greek financial assistance program.”
Jeroen Dijsselbloem said a package of debt measures would be “phased in progressively”, adding that he was “glad to confirm” the IMF would now stay on board.
Poul M. Thomsen, director of the IMF’s European Department, welcomed the recognition that Greek debt was unsustainable and relief was needed.
He warned, however, that the IMF board in Washington still had to agree to the fund’s participation. He also said that the extent of debt relief was still not clear.
The IMF and the Eurogroup have been at odds for months over the issue of reducing Greece’s debt.
Greece’s parliament passed new budget cuts and tax rises at the weekend, in order to unblock much-needed aid to help meet the country’s debt repayments over the coming months.
The bill also created a state privatization fund requested by eurozone finance ministers.
Opponents of the measures demonstrated outside parliament on May 22.
The Greek government, led by the leftist Syriza coalition, agreed to a third bailout worth €86 billion ($96 billion) in 2015.
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