Solskjaer spent 11 seasons at Old Trafford, scoring the winning goal in the 1999 Champions League final.
“Manchester United is in my heart and it’s brilliant to be coming back in this role,” said the Norwegian. This is an opportunity I had to take. I’m really looking forward to working with the very talented squad we have, the staff and everyone at the club.”
Michael Carrick and Kieran McKenna, both part of Mourinho’s coaching staff, will continue to work under Solskjaer.
He was relegated from the Premier League with the Bluebirds during an eight-month spell as manager in 2014, then sacked after a poor start to the Championship campaign.
United will look to appoint a permanent boss at the end of the season.