Finance ministers from the 19-member eurozone approved a package late Friday that will see Greece receive 86 billion euros (USD 96 billion) over three years in exchange for far-reaching pro-market reforms.
The green light for the deal, designed to stop Athens from defaulting on its huge debts and crashing out of the euro, came hours after Greece's parliament voted through the agreement after a bitter all-night debate.
A third of MPs in Tsipras's radical-left party Syriza rebelled against him and he only managed to win the vote with opposition help -- prompting fresh expectations that he will be forced to call early elections.
Syriza swept to power in January on a wave of public anger against steep tax rises, spending cuts and reforms demanded by Athens' creditors -- the EU, European Central Bank and International Monetary Fund -- in exchange for two previous bailouts.
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Critics accuse Tsipras of caving to blackmail from the creditors in agreeing to more painful reforms in exchange for badly-needed cash.
European Commission head Jean-Claude Juncker said Athens had come perilously close to tumbling out of the eurozone and into the unknown, but six months of fraught negotiations had paid off.
Greece will receive a first instalment of 13 billion euros next week, helping cover a debt payment due to the ECB next Thursday.
Eurozone ministers said the first main 26-billion tranche of the bailout will include an "immediate" payment of 10 billion euros to Greece's banks, which are desperately short of cash after panicked customers flocked to withdraw their money.