Solskjær has managed Molde since 2010 and this latest success has sparked renewed conjecture in the local media that he will be snapped up by a Premier League club.
In May he snubbed an offer to coach Aston Villa, preferring to stay at Molde who had never won a title since their inception in 1911 until his arrival.
The 39-year-old was an Old Trafford favourite, scoring 126 goals for United, including an injury-time winner in the 1999 Champions League final against Bayern Munich, in an 11-year career from 1996.
He went on to coach the club's reserves for two years before returning to Norway.
Molde were assured of a successful title defence courtesy of Sunday's 1-0 win over Hønefoss which gave them a four point lead over closest rivals Strømsgodset with a game to spare.