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.
Nahles, a combative, plain-talking former labor minister under Merkel, carries weight in the party base and can hope to shore up support among blue-collar members for another stint in government.
German Foreign Ministry spokesman Steffen Zeibert said in a statement on Monday that the meeting would discuss relations between the two countries and address worldwide issues.
A German official said on Tuesday the country's new government would not change its Brexit stance after Merkel's conservatives and the Social Democrats reached a coalition deal last week.
"She speaks the language of the party base and is therefore the right person to pitch the grand coalition", said Carsten Nickel, a Brussels-based analyst at Teneo Intelligence. Protocol would have dictated that a deputy leader step in as interim chairman.
"The SPD needs an organizational, programmatic and personnel renewal, and I wanted to facilitate that", Schulz told reporters in Berlin in announcing his retreat.
Scholz and Nahles thanked Schulz for his leadership of the party. In a TV interview on Sunday evening Angela Merkel vowed to stay on as chancellor for the full four-year term and defended herself against criticism for conceding the influential finance ministry to the Social Democrats.
Handing over the finance ministry - long the domain of Merkel lieutenant and fiscal hawk Wolfgang Schaeuble - "was one concession too many", fumed lawmaker Wolfgang Bosbach, reflecting a widely held view in the Christian Democratic Union (CDU).