She said she would work to secure more jobs an prosperity, and promised to provide a strong voice for Germany in the EU.
Markel is set to form her fourth government after the opposition Social Democrats (SPD) voted in favour of another grand coalition on Sunday.
Two-thirds of SPD members backed the deal, despite the threat of veto.
The SPD had been split between the party’s leadership, which backed joining the coalition, and its radical youth wing, which did not.
“Almost six months after the election, the people expect something to happen now,” Merkel said in a short statement on Monday.