The victory over Honefoss gave Molde 59 points and an unassailable four-point lead over Stromsgodset with one match to play.
Solskjaer, who won six Premier League titles as a player with Manchester United, said he was delighted with his side's professionalism.
"The boys have been very focused on getting this done. Now we've shown that it can be won two years in a row - without being called Rosenborg," the former striker told Norway's TV2.
Trondheim side Rosenborg, who won 17 Norwegian titles between 1990 and 2010, are in third on 52 points and could still finish second if they win their final game against Honefoss and Stromsgodset lose to relegated Stabaek.
"I'm lucky to have very good players, and we always had faith that we'd succeed," added Solskjaer.
"Now we'll just have to keep going. If we lose players, we'll just have to reinforce."
As Molde struggled to break down Honefoss at home, the title race looked like it would go down to the wire when Stromsgodset took the lead through Abdisalam Ibrahim.
The midfielder, on loan from Manchester City, opened the scoring after 32 minutes against relegation-threatened Sandnes Ulf.
But weak defending at set pieces meant Stromgodset conceded second-half goals to Christian Gytkjaer and Avni Pepa, both from corners, snuffing out their title hopes.
At the Aker Stadion, Solskjaer sent on Nigerian striker Chukwu as a half-time substitute for Davy Angan.
Chukwu repaid his coach's faith by heading a corner in at the far post on the hour to put Solskjaer's side on course for their second title in his two seasons at the helm.