The 29-year-old, who made five appearances for the Billy Goats in an earlier spell at the club between 2009-2011, has signed a contract until the end of the 2020/21 season..
On signing, Terodde spoke of the tough task ahead of him on his return to the Cathedral City: "I had two great years in Cologne and I’m pleased to be back. I took my first steps in professional football here, and I know the special feeling to play at the RheinEnergieSTADION. Of course we have a tough job ahead of us in the second half of the season, but we’ll try everything to avoid relegation."
New sporting director Armin Veh added, "Simon Terodde is physically strong, has quality up front, has proven himself in front of goals for a number of years and is also a really top guy."
Terodde joined Stuttgart in July 2016 and was pivotal in firing the Swabians back up to the top flight at the first attempt, hitting 25 goals to finish as the Bundesliga 2 top scorer for a second successive season, adding to the 25 he struck in the previous campaign for Bochum.
Watch: Terodde was on target when Stuttgart beat local rivals Freiburg 3-0 on Matchday 10
Although he has struggled to replicate that kind of form in the Bundesliga, finding the net just twice in 15 appearances this term, Cologne are convinced of his goalscoring pedigree and will be looking to the forward to help them off the foot of the table, having endured a difficult 2017/18 season so far in which they earned just six points from their first 17 league games.