BERLIN (Reuters) - Members of Germany's Social Democratic party (SPD), which narrowly won a federal election in September, voted on Saturday to back a coalition agreement with the Greens and Free Democrats that should allow the three-way alliance to take over next week.

       The coalition, the first at federal level between the ideologically disparate Greens, the libertarian Free Democrats (FDP) and Olaf Scholz's centre-left SPD, will end 16 years of conservative governments led by Chancellor Angela Merkel.

       Greens and the FDP also need the approval of their members for the deal that the three parties agreed last month. They hope the lower house of parliament, the Bundestag, will vote Scholz in as chancellor on Wednesday.

       The "traffic light" alliance, named after the parties' respective colours, will usher in a new era of relations with Europe, and plans to speed up digitalisation of the continent's biggest economy and put a focus on fighting climate change.

       (Reporting by Emma Thomasson; Editing by Kevin Liffey)