Monday, September 28, 1998 Published at 16:36 GMT 17:36 UK
Schröder and Greens to negotiate coalition
The SPD and the Greens together will have a majority in parliament
Thrashing out the terms of any deal could take days or even weeks.
"We need a coalition agreement that binds everyone without ifs, ands or buts," Mr Schröder added.
Green Party parliamentary leader, Joschka Fischer, said negotiations would be far from easy and would demand compromises on both sides.
Mr Schröder said the three key principles for the Social Democrats in the negotiations would be economic stability, internal security and continuity in foreign policy. Correspondents say a Social-Democrat-Green coalition would nevertheless be the most radical in post-war Germany.
The SPD won about 41% of the vote in Germany's General Election - 6% more than Chancellor Helmut Kohl's Christian Democrats who have governed for the past 16 years.
The so-called "red-green coalition" would give the parties 345 seats in the 669-seat parliament, a clear 21-vote majority.
"I think 21 seats is enough of a majority to form a stable government," Mr Schröder told the German national ZDF television network.
The Greens would also expect to control the environment ministry, and there is speculation that Mr Fischer is eyeing the post of foreign minister.
'Era come to an end'
Mr Kohl lost his home district of Ludwigshafen to the Social Democratic candidate, and said he would not seek re-election as head of the CDU.
Finance Minister Theo Waigel, who leads the CDU's Bavarian sister party the Christian Social Union, has also said he will not run for re-election as chairman of his party.
Mr Schröder described the election result as a generational change, and said his duty was to unite and modernise Germany.
World leaders congratulated Mr Schröder on his victory, with especially warm words from British Prime Minister Tony Blair and the French Prime Minister Lionel Jospin.
The 54-year old victor said his priority will be to tackle record unemployment, which currently stands at more than 10% of the workforce.
He also pledged to maintain strong relations with Germany's allies, such as Britain and France.
However, just how far he can pursue his policies depends largely on his coalition partner.
Parties look ahead
Mr Kohl remains chancellor for a further month, until the new parliament meets to vote in his successor, and there is plenty of time for political manoeuvring before then.
The CDU will begin discussions on who should replace Mr Kohl as leader. Front-runner for the job is Wolfgang Schaeuble, 56, the party's influential parliamentary leader.
He has diplomatically not ruled out a grand coalition with the SPD should Mr Schröder request it, but has said it looks unlikely.
"The grand coalition is a last resort solution when no other majority is possible," he said. "But the way the result looks at the moment, there is another majority."
The CSU has dismissed the idea of co-operating with the SPD, saying it would only strengthen the extreme left and extreme right.
Mr Schröder said he would not consider forming a coalition with the reform communist party, the PDS - who scored 5.1% of the vote, meaning it has passed the 5% mark necessary to return to parliament.