He takes over at Molde from Uwe Rosler, who was in temporary charge, and will start his new role in January ahead of the start of the Norwegian season in March.
"Ole has had a good period with our reserve team, which has given him a foundation to start somewhere else," said United boss Sir Alex Ferguson.
"He feels it is time he went back to Norway, which also helps his family situation.
"He has been a fantastic servant to us and I am sure he will do well.
"He has worked with some really good young players in our reserve team and has contributed to their development.
"Once he gets experience of managing a club in its own right who knows where it will take him?
"Molde is a very progressive club in Norwegian football, so this is a good start for him."
Solskjaer told Molde's official website: "This is a dream job. I discussed my future career with Sir Alex and he advised me to choose a club where there are people that you would like to work with.
"The choice was therefore easy. After 14 years in Manchester, I look forward to coming home to Molde."
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