Merkel welcomed talks the European Union has already started, and said the new German government will hold talks of its own.
Once again, Ms Merkel will preside over a so-called grand coalition between her conservative Christian Democrat Union/Christian Social Union and the centre-left Social Democrats.
Despite a hard start - former SPD head Martin Schulz first refused to enter a grand coalition, then was forced to walk back on his position, prompting his resignation - the parties are now in a position to "work together constructively" and put an end to Germany's "time of uncertainty", Scholz told reporters at a joint press conference alongside Merkel and CSU leader Horst Seehofer.
Merkel's failed attempt to form a coalition with the free-market liberal FDP and environmentalist Greens persuaded the SPD to go back on this decision.
The same parties have governed for the past four years but Wednesday's parliamentary vote comes 171 days - almost double the previous record - after September's election, in which they all lost significant ground.
"I am optimistic that we'll manage it", Merkel said. Following a disastrous election result that came after four years as Merkel's junior coalition partner, the Social Democrats agreed to join the new government only after lengthy internal wrangling.
"That is the job we have and we will fulfill it".