Solskjaer was rewarded with a three-year deal on Thursday after reviving United’s fortunes since taking caretaker charge in December with a run of 14 wins in 19 games.
However, despite that upturn in form, the Red Devils remain 18 points adrift of league leaders Liverpool and 16 off local rivals Manchester City.
Solskjaer won six league titles in his 11 years as a player at Old Trafford and believes it is now his job to make United title winners once more having not won the league since Alex Ferguson retired in 2013.
“To lift the Premier League trophy again is what we expect, what we are used to, what we have done so many times,” said the Norwegian.
“We can’t wait for too many years, but we have to take it step by step. It’s not going to happen overnight catching the 18 points we are behind the top teams now.”
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