Sky Sports revealed earlier in the week that a deal had been agreed and now the young Norwegian has put pen-to-paper.
The 20-year-old, whose substitute appearance at Galatasaray was his first for United this season, will stay at Ewood Park until the New Year.
King, a full Norway international, has featured only twice for the senior side in more than three years at Old Trafford.
"Why waste six weeks of my career in the reserve league for United when I can develop myself and become better at Blackburn?" King told TV2.
"Henning came with an offer I could not refuse. Now I look forward to playing myself into the team, score a few goals, and help Blackburn up the table."
Berg added: "Joshua is a good player who will give us a physical presence, pace and a more rounded squad.
"He will get the chance to prove himself, and regain more match fitness with us the next week."