Mr Schulz was part of Angela Merkel’s recently formed coalition government.
But the Europhile announced his shock resignation in a statement at the party headquarters in Berlin this evening.
Mr Schulz stood down as President of the European Parliamant to challenge Mrs Merkel in last year’s national elections.
He told party officials Andrea Nahles had been unanimously backed to succeed him by the SPD leadership and that members would vote on their choice on April 22.
Mr Schulz leaves a party deeply divided over the coalition deal and the division of ministerial posts and also facing a disastrous slump in opinion polls.
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SPD chiefs have desperately tried to convince the party’s 464,000 members to back the deal in a ballot on which Mrs Merkel’s fourth term hangs.
But many SPD have grave misgivings about sharing power with Mrs Merkel again and if members reject the coalition deal in a March 4 ballot a new election looks the most likely option.
Mr Schulz hinted last week he would quit to allow the party to regroup.
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