The deal "will certainly reduce the uncertainty and strengthen confidence in Europe and in Greece," European Central Bank President Mario Draghi told reporters in Brussels as he left 12 hours of contentious talks between the eurozone's 17 finance ministers and the International Monetary Fund -- their third meeting in three weeks.
About $44.7 billion of the $57.9 billion bailout installment -- delayed multiple times since June -- is expected to be disbursed to Athens Dec. 13, said Jean-Claude Juncker, president of the eurogroup of finance ministers.
The remaining $13.2 billion is expected to be made monthly from January through March 2013, provided Greece continues to fulfill its pledges under the bailout plan, officials said.
Prime Minister Antonis Samaras welcomed the agreement.
"As Greeks, we fought together, and tomorrow a new day begins for all Greeks," he said in Athens.
The deal, which still requires parliamentary approval in some countries, includes a raft of measures intended to cut Greece's debt $52 billion to 124 percent of gross domestic product by 2020, officials said.
IMF Managing Director Christine Lagarde told reporters the agreement would also ensure Greek debt was "substantially lower" than 110 percent of GDP by 2022.
Greece's debt is expected to peak at 190 percent of gross domestic product next year. Without any debt relief it is forecast to hit 144 percent of GDP in 2020 and 133 percent in 2022.
The deal includes alternative ways of giving Greece relief in light of opposition by major creditors such as Germany and the Netherlands to so-called haircuts that would involve forgiving some Greek debt, The New York Times said.
For instance, the IMF loosened its debt target for Greece to 124 percent of GDP by 2020 from 120 percent after Lagarde pressed ministers to agree Greece's debt could be cut through debt buyback, lowering interest rates, lengthening debt-repayment deadlines and returning profits to Greece made on bonds bought by the ECB, the Times said.
The IMF earlier insisted Greece must cut its debt to by 2020 if the country is to nurse itself back to economic health. The IMF, based in Washington, is responsible for about 20 percent of the $319 billion in bailout money that has been promised to Athens to date.
Based on Lagarde's arguments, the deal also includes a 1 percentage-point cut in the interest rate Greece must pay on loans to other eurozone countries, except to those also receiving bailouts, and a 15-year extension of Greece's debt-repayment due dates to other countries and to the eurozone's European Financial Stability Facility bailout fund, Juncker said.
Greece's interest payments on EFSF loans are also to be deferred 10 years, he said.
The Greek Parliament passed a series of deeply unpopular reforms Nov. 8, including a $17.3 billion austerity package, in return for the promised bailout assistance.
"Greece has fully delivered its part of the agreement, so we expect our partners to deliver their part too," Greek Finance Minister Yannis Stournaras said ahead of the meeting Monday.
After the parliaments approve the deal, the finance ministers plan to give a final the disbursement a final OK.