In total 454 members of parliament voted in favour, while 113 rejected the bailout and 18 abstained.
German Finance Minister Wolfgang Schaeuble earlier warned MPs that it would be "irresponsible" to oppose the €86bn ($95bn; £61bn) package.
Chancellor Angela Merkel's centre-right conservative bloc has been divided over the deal.
Prior to the vote nearly 60 of MPs on her side had indicated they would vote against the rescue package.
In total 46 MPs did not attend the session, reports the BBC's Jenny Hill in Berlin.
It is thought a significant proportion are conservatives, who stayed away to avoid defying Mrs Merkel and voting no to the deal.
Mrs Merkel's Christian Democrat (CDU) party and its Bavarian CSU allies hold 504 seats in the 631-seat Bundestag.
Last month, 65 CDU/CSU politicians refused to support even starting negotiations for a third bailout.
IMF assurances
The finance minister told Wednesday's debate in parliament before MPs voted that they should "seize the chance" for a new beginning for Greece.
Mr Schaeuble said: "There is no guarantee that all of this will work and there can always be doubts.
"But considering the fact that the Greek parliament already approved most of the measures, it would be irresponsible not to seize this chance for a new beginning in Greece."
