The former United striker was appointed as the club's caretaker boss in December following the dismissal of Jose Mourinho but will meet the media for the first time as full-time boss in a news conference at 4pm.
Solskjaer has won 14 of his 19 matches in charge, helping to propel United back into the race for a top-four finish.
As well as improving the club's league form, the Norwegian 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."
Ed Woodward, United's executive vice chairman according to skysports, added: "Since coming in as caretaker manager in December, the results Ole has delivered speak for themselves. 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.
A statement on the official twitter handle of the Red Devils confirmed the appointment of the Norwegian:
United had endured their worst start to a campaign in 28 years prior to Solskjaer's arrival and sat 11 points adrift of the Champions League places.
Solskjaer led United to a 5-1 victory over Cardiff in his first fixture in charge, sparking an eight-match winning run in all competitions which included successes at Tottenham and Arsenal.
United also enjoyed a 12-match unbeaten run in the Premier League before suffering their first league defeat under Solskjaer - a 2-0 loss at Arsenal.
United currently sit in fifth place, just two points off fourth-placed Arsenal, as they prepare to host Watford at Old Trafford on Saturday.
Mark F. silveronline24