"It's done. For four months," one said.
An agreement removes the immediate risk of Greece running out of money next month and possibly being forced out of the single currency area. It provides a breathing space for the new leftist-led Athens government to try to negotiate longer-term debt relief with its official creditors.
European Union paymaster Germany, Greece's biggest creditor, had demanded "significant improvements" in reform commitments by Athens before it would accept an extension of euro zone funding.
Euro zone officials said the accord required Greece to submit by Monday a letter to the Eurogroup listing all the policy measures it planned to take during the remainder of the bailout period, to ensure they complied with conditions.
Officials said an outline deal was reached in preparatory talks involving the Greek and German finance ministers, as well as the managing director of the IMF. It was then agreed by the full 19-member Eurogroup, ending weeks of uncertainty.
With the 240 billion euro EU/IMF bailout programme due to expire in little more than a week, Prime Minister Alexis Tsipras voiced confidence of an agreement despite the objections to the request made in a letter to Dijsselbloem.
"I feel certain that the Greek letter for a six-month extension of the loan agreement with the conditionalities that accompany it will be accepted," Tsipras said in a statement to Reuters before the crucial Brussels meeting. Officials said Greece's partners requested the shorter period.
A report by German magazine Der Spiegel that the European Central Bank was making contingency plans for a possible Greek exit from the currency area if the talks fail, on which the ECB declined comment, highlighted the high stakes.
German Chancellor Angela Merkel, speaking after talks in Paris, said all EU partners wanted to keep Greece in the euro but added: "There is a need for significant improvements in the substance of what is being discussed so that we can vote on it in the German Bundestag, for example next week."
The Greeks won sympathy from Italian Prime Minister Matteo Renzi. "I believe that the principle of doing reforms in exchange for more time is just and correct," he said after a meeting of his government in Rome.
REASON FOR SOME OPTIMISM
After preliminary talks with Greek Finance Minister Yanis Varoufakis, German Finance Minister Wolfgang Schaeuble and International Monetary Fund chief Christine Lagarde, Eurogroup chairman Jeroen Dijsselbloem said there was "reason for some optimism" but the search for agreement remained very difficult.
Finance ministers arriving from other euro zone states lined up to insist on more guarantees for creditors that Greece will fulfil the bailout's strict conditions on budget discipline and economic reforms to win their agreement. Athens is determined to loosen austerity to revive its economy.
Tsipras had a long telephone call with Merkel on Thursday and has spoken repeatedly to the leaders of France and Italy in the search for a solution that allows his radical government to fulfil election promises and hold its head high.
"Greece has done everything possible so that we can arrive at a mutually beneficial solution, based on the principle of double respect: respect both to the principle of EU rules and to the electoral result of member states," he said.
Greece could run out of money by the end of March without new external funds, people familiar with the figures say, driving it nearer to the euro zone exit.
Euro zone officials said Greece's track record and the combative behaviour of its new leaders have undermined their confidence in whether Athens will deliver what it agrees to in talks with the other countries sharing the euro.
"Unfortunately the changing rhetoric of the Greek authorities has created a certain erosion of trust, so we must build this once again at this Eurogroup meeting and we are hopeful a solution can be found based on the current programme," European Commission Vice-President Valdis Dombrovskis said.
Some pointed comments were directed at Varoufakis, an outspoken Marxist economist and blogger, and his casual style. "Even hardliners like us have to give the benefit of the doubt to a communist in a Burberry scarf," an official of one hawkish European country joked.
Adding to pressure to reach a deal, Greek savers have withdrawn their money from the banks at an accelerating pace despite government assurances that there is no plan to introduce capital controls to stem the outflows.
Deposit outflows rose to a total of over 1 billion euros in the past two days, some of the highest daily levels seen this year, three senior banking sources told Reuters.
Greeks are nervous before a three-day weekend, given memories of capital controls imposed in Cyprus in 2013 over a long weekend, a senior banker said. Monday is a public holiday in Greece.
Tsipras, elected last month on a platform of scrapping the bailout, says austerity has strangled his country's economy and caused a humanitarian crisis.
Merkel has in the past agreed financial rescues only at the very last moment when she could tell Germans the future of the euro zone was at risk.
Berlin is Greece's biggest creditor, owed 50 billion euros as its share of the EU/IMF bailouts. As Europe's biggest economy, it would take a hit in the turmoil that might ensue if Greece defaulted and left the euro area.
However, whether for tactical reasons or out of deep exasperation with Athens, Germany has conveyed the message that a Greek exit, while not desirable, would be manageable.
The euro rose against the dollar after news of the draft accord on Friday and Greek government bond yields fell on optimism for a debt deal.
