The 20-year-old striker has been scouted by compatriot Henning Berg and given a chance to play regular football in the Championship until January as Rovers look for promotion
The forward is highly rated at Old Trafford but has been given the chance to seek out regular football and continue his development under new manager - and former Red Devils player - Henning Berg.
The 43-year-old coach secured the deal for his 20-year-old Norwegian compatriot on the final day of the Football League loan window, and will strengthen the club as they look to climb from sixth position in the table.
The Oslo-born player was signed by United as a 16-year-old in 2008, but has struggled to break into the first-team squad at Old Trafford.
However, he played in the final five minutes of United's 1-0 Champions League defeat to Galatasaray on Tuesday evening as Sir Alex Ferguson sought to experiment having already qualified for the last 16.
King has had loan spells at Preston North End, German side side Borussia Monchengladbach and made 18 appearances for Hull City last season.
But if the forward wants a spot in Berg's starting XI, he will have to edge out Colin Kazim-Richards, Jordan Rhodes, Ruben Rochina and Nuno Gomes.