Stoger has managed the Billy Goats since 2013 and, after winning promotion, secured European football for the first time in 25 years with a fifth-placed finish in the 2016-17 campaign.
However, this season has seen Koln claim just three points from their opening 14 games and facing an early Europa League exit should they fail to beat Red Star Belgrade on Thursday.
Saturday's 2-2 draw with Schalke 04 kept Koln winless and rooted to the bottom of the Bundesliga table, prompting Stoger to bring his four-year tenure to an end by mutual consent.
"It was clear to us on Friday that the Schalke match would be our last," the 51-year-old told the club's official website.
"We decided to wait until Sunday to communicate this in order to fully concentrate on the match. It is in the best interest of the club and especially the team that a decision was made and clarity restored.
"To the players, the staff at the club, the fans, and the city of Cologne: you have grown dear to the hearts of Manni Schmid (his assistant) and I, we will keep our fingers crossed that my successor manages to keep Cologne in the Bundesliga."
Koln Under-19s coach Stefan Ruthenbeck has taken temporary charge of the senior team until the mid-season break.