The 20-year-old forward initially moved to Ewood Park on loan in November - the only signing of Henning Berg's brief tenure as manager.
Two goals in eight appearances, including the opener in last weekend's 3-1 triumph at Barnsley, have proved enough to earn the Norway international a deal that runs until summer 2015 with the option of a further year.
"I've enjoyed my time here, we've a great group of lads and I think I've settled in well," he said.
"I'm happy to be here and I'm really looking forward to the next two-and-a-half years that I've signed for.
"Everybody has made me so welcome here. I feel comfortable here and I'm happy to make the deal permanent."
- Sports & Recreation
- Henning Berg