Jose Mourinho's two-and-a-half year reign was brought to an abrupt end on Tuesday, having overseen the club's worst start to a Premier League season.
The Portuguese failed in terms of style as well as substance, with United announcing that an interim appointment would be made before bringing in a full-time replacement next summer.
The club quickly worked on recruiting former striker and reserve team boss Solskjaer from Molde, with the club announcing his appointment for the remainder of the 2018-19 campaign within 24 hours of Mourinho's exit.
Mike Phelan, Sir Alex Ferguson's former right-hand man, will join him as first-team coach at Old Trafford, working alongside Michael Carrick and Kieran McKenna.
"Manchester United is in my heart and it's brilliant to be coming back in this role. I'm really looking forward to working with the very talented squad we have, the staff and everyone at the club," Solskjaer told the United website.
Ed Woodward, Executive Vice Chairman, added: "Ole is a club legend with huge experience, both on the pitch and in coaching roles. His history at Manchester United means he lives and breathes the culture here and everyone at the club is delighted to have him and Mike Phelan back. We are confident they will unite the players and the fans as we head into the second half of the season."