The bailout fund will disburse 8.5 billion euros to Greece, they said in a statement.
The latest tranche of the international bailout will help avert a fresh debt crisis in July when the next €7 billion euro repayment of loans becomes due.
The payment is still subject to parliamentary approvals in some countries.
IMF Director Christine Lagarde said she would propose an approval in principle to her executive board.
The International Monetary Fund wants clarity on longer-term debt relief for Greece once the current funding scheme, worth up to 86 billion euros, runs out next year.
Christine Lagarde said the IMF was ready to participate to the third bailout program for Greece after the meeting of eurozone finance ministers in Luxembourg which capped months of negotiations.
However, the IMF could join the program with a financial support “in the range of $2 billion” only after a full deal on additional measures of debt relief for Greece, she said.
Time was beginning to press for this payment. Greece has repayments on other loans due next month, which it could not otherwise have made.
The decision reflects economic policy actions already taken by Greece and the new commitment by the IMF’s managing director Christine Lagarde to recommend that her board contribute financially to this bailout.
An IMF contribution was politically important for Germany, especially to strengthen the perceived credibility of the bailout.
The eurozone group welcomed the financial and structural reforms enacted by Greece, including income tax and pension reform.
Germany’s parliament will discuss the bailout deal on June 16, finance minister Wolfgang Schaeuble said.
Greek finance minister Euclid Tsakalotos said the agreement would allow market access ‘in due course’.
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