Solskjaer took charge of Molde in January and nine months later guided them to the title for the first time since the club was formed 100 years ago.
"It's a good start as a manager," said the striker, who scored 23 goals for Norway and 126 during an 11-year spell with United.
Molde clinched the championship two games from the end of the season on Saturday when Rosenborg, the only side that could overhaul them, lost.
Solskjaer wrote his name in United folklore when he scored the decisive last minute goal that capped United's fightback against Bayern Munich to win the 1999 Champions League final.
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