The 20-year-old striker came through the Manchester United academy, but never made a Premier League appearance for Sir Alex Ferguson's side.
King has spent time on loan at Preston North End, Borussia Monchengladbach and Hull City, but joined Blackburn earlier this season, initially on a temporary basis.
And the Norway international has become one of the first transfers of the 2013 winter window, joining Championship side Blackburn for £1m.
King has hit two goals in eight appearances for Rovers this term, and has been signed by the managerless club, who sit 13th in the English second tier after last season's relegation from the Premier League.
Speaking to the Blackburn club website, King said: "I've enjoyed my time here, we've a great group of lads and I think I've settled in well.
"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, I'm happy to make the deal permanent."
King's only first-team appearance for United came as a substitute during a Carling Cup tie in 2009, and with little prospect of working his way into Ferguson's squad, the young striker decided to drop down a division to get first-team football.
He made his debut for Norway earlier this season, scoring his first goal for his country in their 3-1 win away to Cyprus. But with Robin Van Persie, Danny Welbeck, Wayne Rooney and Javier Hernandez ahead of him in the Old Trafford pecking order, King felt it best to further his career away from Manchester United.