The 30-year-old has been on loan at the Whites this season, becoming a key part of manager Martin Jol's side.
The right-back has made 34 league appearances and represented Germany twice during his career.
Riether thanked his former employers - currently in the second tier of German football - before looking to push on with his new side next season.
"Thanks to the FC," he told the club's official website. "The club and the city have grown on me during my time in the Cologne.
"I am pleased after a first season in England and am focused on my other tasks in Fulham. I wish FC Cologne only the best and the imminent promotion to the Bundesliga."
- Sports & Recreation
- Martin Jol