His departure, after seven months, is thought to have been prompted by a clash of creative styles.
Tucker was recruited from DDB London in September 2007 to work alongside the creative directors Juan Cabral and Micah Walker. Walker has since left.
A Fallon spokeswoman said: "Things haven't worked out as we or Adam had hoped, and he's moving on." She added that there are no current plans to replace him.
Tucker is the latest change to a Fallon creative department that has seen some recent upheaval. Last year, the creative team Matt Doman and Ian Heartfield left to join Beattie McGuinness Bungay, and Walker emigrated to Australia. Since then, TBWA\London's Tony McTear has joined as a creative director.
Tucker was seen as a star signing for Fallon because of his track record for winning awards, including a Cannes gold Lion, five silver Pencils at D&AD and golds at the Campaign Press and Poster awards.
He was the creative director on the Harvey Nichols "cat baseball fight", which won a Press gold for DDB London at last year's Cannes Lions. He was also the creative director on a series of ads for the Financial Times, which won gold for best campaign at the Campaign Press Awards last year.
At DDB, he had a long partnership with Justin Tindall, who quit for The Red Brick Road in 2006. Tucker was promoted to creative director following Tindall's departure.