In total 453 members of parliament voted in favor, while 113 rejected the bailout and 18 abstained.
German Finance Minister Wolfgang Schaeuble earlier warned parliament that it would be “irresponsible” to oppose the €86 billion ($95 billion) package.
Chancellor Angela Merkel’s centre-right conservative bloc has been divided over the deal.
Prior to the vote nearly 60 of Angela Merkel’s members of parliament had indicated they would vote against the rescue package.
In total 47 members of parliament did not attend the session.
Angela Merkel’s Christian Democrat (CDU) party and its Bavarian CSU allies hold 311 seats in the 631-seat Bundestag. Angela Merkel’s coalition partner, the Social Democrats, supported the deal, as did the opposition Greens.
Last month, 65 CDU/CSU politicians refused to support even starting negotiations for a third bailout.
On August 18, the parliaments of Austria, Estonia and Spain backed the bailout.
The Dutch parliament also debated the bailout on August 19, after anti-EU Freedom Party leader Geert Wilders insisted members of parliament should be recalled from their summer recess.
The vote by German parliament was the final hurdle before the first installment of the package – €13 billion – could be released, in time for Greece to repay €3.2 billion on August 20 to the European Central Bank (ECB).
Doubts remain about the Greek government’s commitment to the bailout conditions because it previously pledged to oppose austerity.
In exchange for the bailout – and keeping Greece in the euro – PM Alexis Tsipras agreed to further painful state sector cuts, including far-reaching pension reforms.
The new loans will be spread over the next three years. The first tranche of €26 billion will include €10 billion to recapitalize Greek banks.
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