Steinmeier has for some time been manoeuvring for position to lead the party against Chancellor Angela Merkel and the Christian Democrat Union, CDU, in next year's federal election.
On Sunday Beck walked out of a meeting of the SPD leadership just minutes after it had begun, according to Der Spiegel, and resigned as chairman of the party.
He will be succeeded by former Vice Chancellor Franz Münterfering, who had that job from 2004 to 2005 and is hugely respected with the party. He stepped down from national politics last November to care for his ill wife Ankepetra but returned to the national stage in July after she died.
The leadership meeting at a hotel in Schwielowsee, Brandenburg, was supposed to be concentrating on party manifesto policy subject, with the chancellor candidate question held over until after the Bavarian state election at the end of the month.
But the chaos within the party, and the desire by many to get rid of the disastrously unpopular Beck obviously overtook such planning.
The choice of Steinmeier to run against Merkel will open up the until-now half hidden battle between the Chancellor and Foreign Minister for popularity.
It is likely to further paralyse the coalition government which is widely seen to be on its last legs with often open hostility between ministers from different parties.