The first disbursement will take place Dec. 13, said Jean-Claude Juncker, head of the eurogroup of Finance Ministers, which made the decision early Tuesday.
Mario Draghi, President of the European Central Bank, welcomed the agreement.
"It will certainly reduce the uncertainty and strengthen confidence in Europe and in Greece," Draghi said.
This was the third time in the last two weeks that finance ministers from the eurozone had tried to hammer out a deal on the next installment of bailout money - some €44.6 billion ($57.8 billion).
The so-called troika of the European Central Bank, IMF and the European Commission, which is the 27-country EU's executive arm, have twice agreed to bail out Greece, pledging a total of €240 billion in rescue loans - of which the country has received about €150 billion so far. In return for its bailout loans, Greece has had to impose several rounds of austerity measures and submit its economy to scrutiny.
Greece is predicted to enter its sixth year of recession shortly, and there had been fears that it might be forced to drop out of the eurozone, destabilizing other countries in the process.
The main aim of the bailout program is to right Greece's economy and get it to a point where it can independently raise money on the debt markets. It has been clear for months that the country is far from achieving that goal, and the latest talks were about trying to get Greece back on the path to sustainability.
Juncker said the agreement includes:
- A plan to reduce Greece's debt level to 124 percent of its gross domestic product by 2020 and below 110 percent by 2022. The original goal had been 120 percent of GDP in 2020.
-A lowering by 100 basis points of the interest rate charged to Greece by other eurozone member states - excluding those that are also receiving bailouts.
-A 15-year extension of the maturities of loans from other countries and the eurozone's bailout fund, the European Financial Stability Facility, and a deferral of interest payments by Greece on EFSF loans by 10 years.
"This is not just about money," Juncker said. "It is the promise of a better future for the Greek people and for the euro area as a whole."
The head of the IMF, Christine Lagarde, also said the agreement was significant.
"We wanted to make sure that Greece was back on track," Lagarde said. "If you put it all together it is a significant amount."
Greek officials welcomed the agreement.
"Of course it is positive that the blockage has been removed from the loan installments," said Notis Mitarakis, the country's deputy development minister, early Tuesday, on the private Skai channel in Greece. "But I am unaware of the details, so we'll have to look at them."
The channel reported that Greece would get €31.5 billion ($40.84 billion) straight away and the rest in separate installments in January, February and March, but it cited no sources.
The political agreement reached Tuesday will have to be submitted to national parliaments in some countries. After that, the finance ministers plan to hold another meeting, either in person or by telephone, to give final approval to the disbursement.