The Norway winger would have been able to walk free from Ewood Park after his contract had come to a close and Big Sam admits he would have been almost impossible to replace.
"Like most things, it was a long, drawn-out affair, but we got to a position where we didn't really want to lose him and in the end I think he didn't really want to go," he told the Rovers website.
"Finally, it came to a mediation of falling between what we wanted to give him and what he wanted, so I'm glad to see that he's put pen to paper because he's a vastly experienced player.
"It's like signing a free transfer really, that's what it equates to. He's out of contract and he's re-signed without us having to pay a transfer fee for him. Had he left, we would probably have had to find £4-6m to replace him."