BERLIN (Reuters) - Germany's Social Democrats (SPD), Greens and Free Democrats (FDP) signed a coalition deal on Tuesday that sets out how to accelerate a green transition and modernise Europe's biggest economy when they take office this week.

       The alliance between the unlikely bedfellows, the first such grouping at a national level, brings to an end 16 years of conservative-led government under Angela Merkel who did not stand for a fifth term in a September election.

       The SPD's Olaf Scholz is due to be elected chancellor by the Bundestag lower house of parliament and officially take office on Wednesday.

       Under the logo "Dare More Progress", leading members of all three parties signed the 177-page agreement in front of television cameras.

       "This should be a morning for a new start," Scholz said.

       FDP leader Christian Lindner said the last few weeks had been about talking and now it was time for action.

       "From this week we want to work on making progress. We are under no illusion, we face big challenges," he said.

       The parties presented the agreement last month but needed members to approve it before signing it.

       (′Writing by Madeline Chambers; Editing by Nick Macfie)