
Torum's resignation less than 24 hours after his side defeated visiting Spanish team Valencia 2-0 in the Champions League.
Rosenborg, league champions in 2006, currently lie sixth in the league standings.
An emotional Torum choked several times at a news conference when he made the announcement.
Trond Henriksen was to take over for the rest of the season along with Kare Ingebrigtsen, the Trondheim-based club said.
Torum was reported to have had a rocky relationship with sports director Knut Thorbjorn Eggen.
The club said it decided to terminate Torum's contract as it had hoped to fare better in the league.
Chairman Terje Svendsen told Rosenborg's own web site that "we don't solely blame the trainer," noting that last season Torum "saved the club."
DPA