Prime Minister Antonis Samaras described a deal struck during the early hours of Tuesday morning between the eurozone and the International Monetary Fund as one that would secure Greece’s place in the single currency by releasing more bailout funding and reducing its debt significantly in the years to come.

Samaras and his coalition partners showed themselves to be pleased with the outcome of the deal in Brussels, where eurozone finance ministers and the IMF struck on a formula that would reduce Greek debt from a projected 189 percent of GDP next year to 124 percent in 2020 and lower than 110 percent by 2022.

The agreement will lead to several methods being adopted to reduce Greek debt. These include reducing by 1 percentage point to 0.69 percent the annual interest rate charged by other eurozone members for bilateral loans to Athens and extending by 15 years the maturities and deferring for 10 years the interest on loans from Greece’s second bailout.

Also, the European Central Bank will return via national central banks the profits it makes on Greek bonds purchased through its SMP program, and Greece will launch a program to buy back at 28 to 30 cents on the euro some 63 billion euros in privately-held government bonds. This should reduce debt by about 20 billion euros, or 11 percent of GDP.

The plan also allows for further measures to reduce Greek debt to be taken once it produces primary surpluses.

A number of details regarding how the debt reduction program, particularly the bond buyback, will work were not clarified after the Eurogroup. Greece, for instance, will need about 10 billion euros to execute the purchase of its bonds from investors but it’s not clear how it will get this money.

Also, there is no certainty that the buyback will hit the targets that the eurozone finance ministers used to calculate the trajectory of Greek debt over the next few years. IMF Managing Director Christine Lagarde said that the Fund would not approve the release of its part of the loan tranche in mid-December until the buyback has been completed.

The Eurogroup agreed to release next month just 34.4 billion euros of the 43.7 billion Athens was due to receive this year. The remaining 9.3 billion euros will be released in three tranches at the beginning of 2013.

In a televised speech on Tuesday night, Samaras welcomed the Eurogroup deal, saying that it signaled “the end of a very dark period for Greece.” He said the agreement had helped Greece to “regain its credibility, lay the foundations for Greek debt to become sustainable and secure its position in the eurozone,” adding that it “rewards the sacrifices of the Greek people and opens the road to growth.”

Socialist PASOK leader Evangelos Venizelos was more cautiously optimistic, describing the deal as “undoubtedly positive” in a speech to his MPs but noting that certain details required consideration such as the terms of a bond buyback scheme.

Democratic Left leader Fotis Kouvelis welcomed the deal as “decisive step toward securing the country’s continued presence in the eurozone.”

The three leaders are to meet at 10 a.m. on Wednesday ahead of a cabinet meeting scheduled for 1 p.m.