Mike Phelan, Solskjaer's assistant, will be also be staying on at United but his contract has still to be arranged. United are expected to make a "gesture of good will" to Molde following Solskjaer's appointment, which could include a friendly match, although the details are still to be sorted out. The Norwegian club agreed to release Solskjaer from his contract when United requested he take temporary charge and will now have to settle on a permanent replacement.
"From the first day I arrived, I felt at home at this special club," said Solskjær. "It was an honour to be a Manchester United player, and then to start my coaching career here.
"The last few months have been a fantastic experience and I want to thank all of the coaches, players and staff for the work we've done so far.
"This is the job that I always dreamed of doing and I'm beyond excited to have the chance to lead the club long-term and hopefully deliver the continued success that our amazing fans deserve.
"It feels great. It's been three fantastic months and the support I got here, from the chats I've had with Ed, the owners, the staff in and around here, has been great.
"It's truly an honour. I think everyone knows, and I've spoken about it in the last few months, that this is the dream job for any football-interested man, especially anyone who has been involved with Manchester United.
"Being given the opportunity now to move the club forward, with all the potential there is, it's fantastic.
"We want to be challenging for every season from now on, and I wouldn't have said 'yes' if I wasn't looking forward to it and if I didn't believe in the club, in the potential and in what we're doing.
"And I hope and I feel I can do this job justice. That's the first thing I said to myself when I got the call a few months back, and hopefully now I can even improve on it."
Ed Woodward, United's executive vice-chairman, said Solskjaer had a "deep understanding of the culture of the club" that proved an influential factor behind his appointment. Mourinho was often criticised for failing to properly understand United's philosophy.
"Since coming in as caretaker manager in December, the results Ole has delivered speak for themselves," Woodward said.
"More than just performances and results, Ole brings a wealth of experience, both as a player and as a coach, coupled with a desire to give young players their chance and a deep understanding of the culture of the club.
"This all means that he is the right person to take Manchester United forward. I want to thank Ole and the coaching team for everything they have done so far and congratulate him on this richly deserved appointment. The fans and everyone at the club are behind him as he looks to take us where we need to be and build the next stage of our history."
Solskjaer will now be joined by his wife and three children, who will move to England from Norway.
"We've really enjoyed the last eight years in Norway, living there of course, so it's going to be a change for them, but we're looking forward to it," said Solskjaer.
"These six months – or three months as it is now - that we agreed on as a family that we'd do separately, because there was any use or need to move them over, that's gone now, now we can move in together.
"We started building a house in 2007, finally maybe in 2019 we can move into it. That's long-planning!"
