The 28-year-old was signed from Aalborg in January last year for £2million but he has since failed to establish himself under Roy Keane and now Ricky Sbragia.
After making just six substitute appearances last season and none this term the Sweden international has decided to call time on his short stay at the Stadium of Light.
Things started brightly with Prica after he managed to score on his debut against Birmingham but opportunities became few and far between for the former Helsingborgs youngster.
The Black Cats allowed the frontman to hold talks in Norway and a deal has now been agreed.
Prica has signed just in time for the start of the Norwegian campaign with Rosenborg facing Valerenga this weekend in the season opener.