Solskjaer, the former Manchester United striker, lifted Molde to 55 points with two rounds left to play, seven more than Tromso and nine ahead of Rosenborg.
On a dramatic day, Molde looked like securing the title with a victory over Stromsgodset until a last-minute equaliser from Anders Agnes Konradsen postponed the party at the Aker Stadium.
Rosenborg kicked off against Brann knowing they needed a victory to keep their slim hopes alive, but they looked nothing like title contenders as they conceded three goals in the first 20 minutes on the way to a 6-3 defeat.
Founded in 1911, Molde had finished runners-up in the Tippeligaen on seven occasions but it took the return of the talismanic Solskjaer to deliver the title the club had craved.
Despite scoring 33 goals in 42 matches for Molde before moving on to a glittering career at Manchester United, Solskjaer had never won a major trophy in his native country.
He took over as manager at Molde in January 2011 following a successful stint as reserve team coach at United but suffered a rocky start on his return to Norway.
Molde lost his first league game to promoted Sarpsborg 08, before draws against Tromso and Viking left his side with just two points from a possible nine.
Solskjaer, famed for his ability to come off the bench and change a game as he did when he scored in stoppage-time to secure United's dramatic Champions League final victory over Bayern Munich in 1999, turned the team's fortunes around.
Victory at rivals Tromso on October 2 put Molde in pole position in the title race and draws against Odd Grenland, Stabaek and Stromsgodset secured the trophy.
