She sought to allay fears among conservatives that by ceding the finance ministry, the next government will stray from the strict fiscal discipline enforced by former finance ministerWolfgang Schaeuble.
The Social Democrats last week reached a coalition government deal with Merkel's bloc that is widely viewed as favorable to the party.
Merkel also described leaving the finance minister post to the SPD as a "painful" but "acceptable" price paid by her CDU party to form a coalition government.
Scholz and Nahles thanked Schulz for his leadership of the party.
This comes as the leader of the SPD Mr Schulz will hand over the role of leader of the SPD to Andrea Nahles.
Seeking to end the infighting, chairman Martin Schulz said Tuesday that he was resigning effective immediately.
Angela Merkel's conservative alliance took a drubbing in last year's election where the right-wing Alternative for Germany Party (AfD) made big gains, ending up in third place on the strength of popular discontent about her decision to open the country's doors to over a million migrants. But expectations that she would take over with immediate effect on a caretaker basis until a party conference triggered resistance as it breached party procedure.
"If I can contribute to that by resigning, it will have been worth it", he said outside the SPD headquarters.
"Of course the list will draw from party's entire spectrum", Merkel told public broadcaster ZDF in the interview.
Two sources in the SPD leadership said the party decided not to make Ms Nahles a caretaker leader because it did not want to pre-empt a vote at the party congress and so possibly influence the members' vote on a coalition.
Mr Schulz, 62, ditched plans to take the post of foreign minister after fierce criticism from some former allies, not least because he had pledged not to serve in a cabinet with Ms Merkel. As a result of the pact, the CDU will occupy the ministries of Economy and Energy, Education and Investigation; Agriculture and Food; Defense and Health.
The coalition deal has yet to be approved by the SPD's approximately 460,000 members, whose verdict will be announced on 4 March.