"On this basis, Greece is and will irreversibly remain a member of the euro area," said European Commission President Jean-Claude Juncker after the deal was sealed.
The final rescue package would eventually give Greece up to 86 billion euros ($93 billion) in loans over three years in exchange for harsh spending cuts and tax hikes.
The deal must still be approved by some national parliaments, including Germany, but that is largely considered to be a formality. Some nations, such as Finland, have already given their approval.
The move saves Greece from a disorderly default on its debts which could have come as soon as next week and helps to cement its membership of Europe's single currency, but means more hardship for ordinary Greeks.
The approval came after Greece's parliament passed a slew of painful reforms and spending cuts after a marathon overnight session that divided the governing party, raising the specter of early elections.
The bailout bill passed through the parliament thanks to support from opposition parties, with 222 votes in favor, 64 against, 11 abstentions and three absent in the 300-member parliament.
Although approved by a comfortable majority, the result was a blow to Prime Minister Alexis Tsipras, who saw more than 40 of his 149 radical left Syriza party lawmakers vote against him. He has come under intense criticism from party hardliners for capitulating to the creditors' demands for budget cuts — austerity measures he had promised to oppose when he won elections in January.
The bill includes reforms increasing personal, company and shipping taxes, reducing some pensions, abolishing tax breaks for some groups considered vulnerable and implementing deep spending cuts, including to the armed forces.
State television said Tsipras was expected to call a vote of confidence in his government, but that was not confirmed. Government spokeswoman Olga Gerovasili said any action would come after Aug. 20, when Greece has to make a large debt repayment to the European Central Bank.
Tsipras has maintained his public popularity in Greece despite his U-turn on austerity policies, and consistently leads opposition parties in opinion polls. An election would allow him to remove the hard line elements from his party, but it is not a risk-free option.
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