Eurozone finance ministers have agreed a new bailout deal for Greece worth up to €86 billion (£61bn) over the next three years.
It comes after Greek MPs on Friday backed the new bailout package, aimed at helping rebuild Greece's economy.
The move saves Greece from a defaulting on its debts which could have come as soon as next week.
European Commission President Jean-Claude Juncker said: "On this basis, Greece is and will irreversibly remain a member of the euro area."
The Greek stock market has reopened after a five-week shutdown amid the country's financial crisis, with stock prices falling sharply.
The main index was down nearly 23 per cent in early trading.
National Bank of Greece, the country's largest commercial bank, was down 30 percent, which is the daily limit.
Trading on the Athens stock exchange was suspended late in June as part of capital controls imposed to stem the flow of money out of the country.
The German parliament has approved a deal to extend Greece's financial bailout by four months.
A total of 542 MPs within the 631-seat chamber voted in favour of approving the extension.
The approval came after Finance Minister Wolfgang Schaeuble - a sceptic of Athens - promised Greece would not be allowed to "blackmail" its European partners.
The vote in the Bundestag was the only major hurdle for the four-month exension for the most heavily indebted country in the euro zone.
Greece hopes that it will be able to start discussions with its EU and International Monetary Fund partners on filling the state's funding gap straight away, a finance ministry official has said.
Speaking on the condition of anonymity, the official said:
The discussions on Greece's funding gap will begin tonight, tomorrow morning.
Greece's reform plan is sufficient for the Eurozone to continue to give the country aid, but is lacking finer details, International Monetary Fund chief Christine Lagarde has said.
In a letter to Eurogroup president Jeroen Dijsselbloem, Ms Lagarde said that the Greek plan was comprehensive in some areas but "not very specific."
In quite a few areas, however, including perhaps the most important ones, the letter is not conveying clear assurances that the government intends to undertake the reforms envisage.
Among other areas of concern, she cited pensions and value-added tax policy as well as labor market reforms.
Euro zone finance ministers have agreed that a Greek request for a bailout extension could now go ahead, subject to approval by member state parliaments.
The European Commission vice president for the euro said on Twitter that the ministers had agreed to the extension via a telephone conference.
Greece's finance minister Yanis Varoufakis said he was pleased with the agreement reached with Eurozone ministers. He said he believes the interest of "the average European above all else" has been served, and that the commitments his country has made are ones his government "wanted to make anyway".
He said: "The weekend will be one of joy and creativity. We are writing our own reforms, with our partners."
IMF Chief Christine Lagarde has welcomed the deal reached between the Greek authorities and the Eurozone finance ministers.
Speaking in Brussels she said the negotiations have been labourious but constructive, and have resulted in a "timeline" for the necessary changes that need to be made. She said the IMF is pleased that work can now begin.
Finance minister Yanis Varoufakis said Greece "combined logic and ideology in the way we negotiated" to reach the bailout deal.
ITV News Economics Editor Richard Edgar reports:
Man of the moment, Greek Finance Minister says "Greece has turned a page"(with a shiny head in foreground) http://t.co/2OV3znqEdh
Tiny room packed with international press. "We combined logic and ideology in the way we negotiated" says Varoufakis http://t.co/zZUGCISyJi