The former United striker, who was appointed as the club’s caretaker boss in December following the dismissal of Jose Mourinho, has won 14 of his 19 matches in charge, helping to propel United back into the race for a top-four finish.
Solskjaer, apart from improving the club’s league form masterminded a memorable comeback in the Champions League last-16 tie against PSG earlier this month, with United overturning a two-goal first-leg deficit to set up a quarter-final tie against Barcelona.
“From the first day I arrived, I felt at home at this special club,” Solskjaer told the club’s website.
“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.”