The Bundestag vote cleared one of the final obstacles to Greece getting funding so that it can make a 3.2 billion-euro debt repayment to the European Central Bank on August 20.
But a sizeable number of conservative lawmakers rebelled against Chancellor Angela Merkel, objecting to pouring yet more billions into Greece.
The Dutch parliament also gave its blessing to the Greek rescue, while the board of the euro zone's bailout fund in a teleconference approved disbursing the first tranche of funds under the new Greek program.
In Athens, Prime Minister Alexis Tsipras and his inner circle debated whether to take on anti-bailout rebels in his own radical left Syriza party by calling a parliamentary confidence vote or to go straight to early elections.
Popular misgivings about more aid for Athens run deep in Germany, the euro zone country which has already contributed most to Greece's two previous bailouts since 2010.
But Tsipras secured the third program by promising to impose reform and austerity policies that are so onerous that a sizeable number of Syriza lawmakers rejected the deal in parliament on August 14.