Germany’s parliament earlier approved her re-election by 364 votes to 315.
Mrs Merkel has vowed to get to work quickly after the longest period of coalition-building in post-war Germany.
It is nearly six months since the election. Mrs Merkel’s conservative CDU/CSU bloc had its worst result in almost 70 years.
But she finally secured a coalition deal with the Social Democrats (SPD) earlier this month following a painful stretch of political deadlock.
It cost her several key posts – including finance and foreign minister – in Germany’s new cabinet.
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After parliament confirmed Mrs Merkel’s reappointment on Wednesday, she told MPs: “I accept the vote.”
Her scientist husband, Joachim Sauer, and her 89-year-old mother Herlind Kasner were among the well-wishers in the Bundestag’s lower house.
But analysts said the vote was a humbling start as only 364 MPs backed her appointment, when her conservative bloc and the SPDs have 399.
Mrs Merkel was formally appointed by President Frank-Walter Steinmeier before taking the oath of office.
Mainstream parties suffered in September’s election amid a surge by right-wing populists.
The anti-immigrant party, Alternative for Germany (AfD), entered the federal parliament for the first time with just over 12% of the vote, and now makes up the largest opposition group.