"The SPD needs renewal in its organization, in its personnel, and in its programme," Schulz said as he announced his departure.
"I think we've made a good decision" in picking Nahles for the top job, he added.
"I would dearly like to take up the responsibility that I've been offered" in service to party and country, Nahles later told journalists.
If elected at a party congress on April 22nd, Nahles would become the first woman to lead the 153-year-old party, which expects to soon renew its coalition with Chancellor Angela Merkel's conservatives.
But hopes she could immediately become provisional SPD leader were dashed by anger in the SPD base at what many saw as a leadership backroom deal rather than an open vote.
Steve Hudson, of the party's #NoGroKo group, charged that the leadership's proposal for a single candidate evoked North Korean politics and said the party "doesn't belong to a small group of top functionaries in Berlin who can do what they want".
Meanwhile, Nahles' coronation is no longer unchallenged after last-minute candidate Simone Lange, the 41-year-old mayor of northern city Flensburg, threw her hat into the ring.
Until April, Hamburg mayor Olaf Scholz will lead the centre-left on a caretaker basis.
Germany's second-biggest party has been torn by bitter infighting and is deeply demoralized since it scored its worst post-war election result of 20.5 percent last September.
Its left and youth wings and some regional chapters are in open revolt against SPD plans to again govern as junior partner to Merkel, with the deal for a so-called GroKo alliance still subject to a vote by its 470,000 rank-and file members.
Schulz last week said he would hand over the top job to Nahles, then announced he would claim the foreign minister's job from his estranged former ally Sigmar Gabriel -- a move he was reversed after a party outcry.
With Schulz and Gabriel's political careers in tatters, Nahles looks set to claim the chair burdened with the task of revive the spirit and electoral prospects of the labour party.
The 47-year-old former labour minister with a reputation for hard work and brash comments will have her work cut out, as a poll in Bild daily said support for the SPD had sunk to a record low of 16.5 percent.
The rise of party veteran Nahles may mean that, together with Merkel, women will head both of Germany's two big mainstream parties -- a move hailed by Mona Kueppers, who heads the National Council of German Women's Organisations.
Within the SPD, too, the time is ripe for a female leader," Kueppers told AFP. "The fact that the party has competent women for the job has been well known for a long time."