The coalition between her centre-right CDU/CSU bloc and the Social Democrats (SPD) has a huge majority, with 504 of the 631 seats in the lower house.
Angela Merkel was confirmed by 462 votes, with nine abstentions.
Germany’s tough stance on fiscal discipline is unlikely to change under the new coalition.
The SPD’s membership voted on Sunday to back the coalition after painstaking negotiations.
The party hammered out a minimum national wage, an hourly rate of 8.50 euros ($11.55) that will come into force for the first time in 2015.
The new government will be slightly to the left of the previous one, in which the Christian Democrats/Christian Social Union were in coalition with the market-oriented Free Democrats (FDP).
But the SPD will form a minority part of the government and no-one doubts that Chancellor Angela Merkel will be in charge.
As the EU’s most industrialized and populous state, with its biggest economy, Germany dominates decision-making for the eurozone.
For Tuesday’s vote, 621 members of the Bundestag were present, of whom 150 voted against Angela Merkel.
Between them, the Left Party and the Greens have 127 seats, so at least 23 of those who rejected her nomination were from the parties making up the new coalition.
The coalition talks had been the longest for any German government since World War II.
The CDU/CSU and SPD finally signed the deal, a 185-page agreement entitled “Shaping Germany’s Future”, late last month.
Angela Merkel was obliged to turn to the SPD after the FDP failed to win any seats in the 22 September election, falling short of the 5% hurdle to enter the Bundestag.
Trusted Angela Merkel ally Wolfgang Schaeuble will remain finance minister in the new government, one of 10 CDU/CSU politicians in the 16-strong cabinet.
“His name stands for euro stability and I’m glad that he’s continuing,” Angela Merkel said after news of the new line-up emerged.
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