The Eurogroup announced its agreement on Tuesday following a teleconference call during which Greece’s reform package put forward by Athens earlıer in the day was discussed.
The Eurogroup said in a statement: "The (Troika) institutions provided us with their first view that they consider this list of measures to be sufficiently comprehensive to be a valid starting point for a successful conclusion of the review.
"We therefore agreed to proceed with the national procedures with a view to reaching the final decision on the extension by up to four months of the current Master Financial Assistance Facility Agreement."
The EU’s executive body, the European Commission, has also signed off Greece’s reform proposals earlıer on Tuesday, saying the list submitted on Sunday morning was "sufficiently comprehensive to be a valid starting point".
The statement added: "We call on the Greek authorities to further develop and broaden the list of reform measures, based on the current arrangement, in close coordination with the institutions in order to allow for a speedy and successful conclusion of the review."
The decision saves Greece from the risk of running out of cash by the end of the month and exiting the euro zone in a so-called "Grexit".
The President of the Eurogroup, Jeroen Dijsselbloem, earlier told the European Parliament ahead of the Eurogroup conference that although Greece was serious about its reform commitments, it would take time to agree on the details of its reform plans.
Dijsselbloem said: "I think they’re very serious, but it’s a new Greek government with a different political vision than the previous one.
"Therefore they want changes with the agreement."
The move came after the new leftist government in Greece made a full-scale commitment to the Eurogroup bailout program which it had campaigned against ahead of its election in January.
In a letter from Greek Finance Minister Yanis Varoufakis to Eurogroup head Jeroen Dijisselbloem, which was leaked to the Reuters news agency on Tuesday, the radical economist promised to strictly observe the program set out by Greece's Troika creditors of the IMF, European Central Bank and European Commission - the very plan that his party SYRIZA had campaigned against as it sought to woo voters ahead of national elections.
The letter promised to allow ongoing privatisations and leave alone those already completed, to maintain fiscal targets and not to change any reforms put through in the past.
The Greek government wishes to boost welfare spending, but Varoufakis promised in the letter to see that this does not involve "dangerous spending".
The approval came after the German government requested from parliament on Tuesday an extension of the Greek bailout program, made conditional upon Greece's completion of the review process by creditors.
The German parliament is expected to vote on the motion at some point this week.