The former United striker will take charge of the first team with immediate effect and will remain in place while the club looks for a new full-time manager.
He will be joined by Mike Phelan as first-team coach, 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," said the Norwegian.
Executive vice chairman Ed Woodward said: "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."