Merkel now heads a "grand coalition" of Germany's biggest parties – her conservative Union bloc and the center-left Social Democrats, which are traditional rivals. Parliament's lower house elected her as chancellor by 462 votes to 150, with nine abstentions.
The new government will move Germany somewhat leftward, for example introducing a national minimum wage, but will take a largely unchanged approach to Europe's debt crisis.
It features Germany's first female defence minister, conservative Ursula von der Leyen, and sees former foreign minister Frank-Walter Steinmeier, a Social Democrat, return to his old job. Finance minister Wolfgang Schäuble, a powerful figure in Europe's debt crisis, is staying on.
The parties' effort to form a government after national elections on 22 September, in which Merkel's conservatives came close to a parliamentary majority but saw their previous coalition partners lose all their seats, has been the longest in post-second world war Germany.
It was extended by the Social Democrats' decision to put the coalition deal to a ballot of all their members. They won approval last weekend but some remain wary because the party emerged weakened from a previous grand coalition in Merkel's first term, from 2005 to 2009.
At least 42 government politicians didn't vote for the chancellor on Tuesday but, given the new coalition's enormous majority, that is unlikely to worry her.
Conservatives and Social Democrats hold 504 of the 631 seats. Germany's best-known ex-communist, Gregor Gysi, becomes the opposition leader; his hardline Left party is the bigger of two left-leaning opposition groups.
Germany's biggest-selling newspaper, Bild, declared on Tuesday's front page: "Dear grand coalition, we are your extraparliamentary opposition now!" Editor Kai Diekmann wrote that "this parliament is too weak; its opposition too small and too left-wing."