Solskjaer is United's fourth permanent manager since Sir Alex Ferguson retired in 2013
Ole Gunnar Solskjaer says managing Manchester United is his "ultimate dream", and admits Sir Alex Ferguson was one of the first people he called after his position was made permanent.
The former United striker signed a three-year contract on Thursday, having arrived on an interim basis in December to replace Jose Mourinho.
Under the Norwegian, 46, United have lost only once in 13 league games.
"This has been my ultimate dream, maybe a naive dream," he said.
"But I've always had that dream in my mind.
"It's a huge, fantastic family of a football club and I'm so honoured to be given the responsibility."
Solskjaer spent 11 seasons as a United player, scoring the winning goal in the 1999 Champions League final.
When he took charge, United were sixth in the Premier League and 11 points off the top four. They are now just two points behind Arsenal, who occupy the final Champions League qualifying spot.
He became the first United manager to win his first six league games, beating a record held by Sir Matt Busby.
"I'm just going to be myself as I've always been. I know the trade of course. I want us to lift trophies but I can't wait to get to the challenge of improving the squad," Solskjaer said.
"We have worked with them, for three months and the improvement is there to be seen. We know there is so much more to come from them.
"Every day in training the attitude has been fantastic but we know we've a long way to go. It's going to be a mountain to climb but we've climbed a few mountains before."
'We expect to lift the Premier League trophy again'
United have not won the Premier League since 2013 - Ferguson's final season in charge - though they finished second behind Manchester City last term under Mourinho.
When Solskjaer returned to the club, United's points tally was closer to the bottom of the league than the top, but he has since led them to victories at Tottenham, Arsenal and Chelsea, with a top-four finish now within their grasp.
Solskjaer's aim is to one day lead United back to the top of the table but he admits it may take some time.
"To lift the Premier League trophy again is what we expect, what we're used to, what we have done so many times," he said.
"We can't wait too many years but it's not going to happen overnight.
"I know we will be successful but it's about taking it step by step.
"What I have done before as a player doesn't really bother me because I am always looking forward.
"It was fantastic to work with the best manager in the world but now I am working here as the manager and I think that's a bigger achievement."
