The former Norway striker scored 126 goals in 366 matches for United between 2006 and 2007. He became United's reserve team coach a decade ago before moving to Norway to manage FC Molde.
Mike Phelan - Sir Alex Ferguson's assistant between 2008-2013 - returns to Old Trafford as Solskjaer's assistant coach 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 Solskjær on the club's website.
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United 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.
Molde have said in a statement that they expect their coach to return to manage them after his six-month spell ends at Old Trafford next May.
"That Manchester United ask Molde FK to lend the manager is by itself an event, and not least a statement of trust for both Ole Gunnar and Molde FK. We are positive to lend Ole Gunnar, we wish both him and the club a success, said Molde CEO Øystein Neerland.
"This is a big opportunity for Molde FK, we think it will be developing and helping to put Molde FK further on the football card,"
United have endured their worst points return after 17 matches in the Premier League era, with Sunday’s chastening 3-1 loss at Liverpool leaving them 19 points behind their bitter rivals.
They also face an eye-watering 11-point gap to the top four, leading the club to dismiss Mourinho at the end of a year that started with handing him a contract extension.
Solskjaer had 11 years at United as a player, memorably scoring in the Champions League final against Bayern Munich to seal the treble in 1999, and spent a period as their reserve coach, working with the likes of Paul Pogba.
The 45-year-old left for his first spell at Molde and, after an ill-fated spell at the helm of Saturday’s opponents Cardiff during which the side won nine of 30 games, returned to the Norwegian club and finished second, qualifying for the second qualifying round of the Europa League.
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For the Norwegian press, this is the biggest story for decades. One commentator in VG made references to Gro Harlem Brundtland leading WHO and Jens Stoltenberg as head of NATO.
The last year in Molde has been a little bit of a roller coaster. After a slow start of the season in Eliteserien, Molde was one of the biggest form teams this fall. Experts were tipping Molde to be the biggest contender to Rosenborg next year – by far. With Molde losing Solskjær until the summer, people are wondering how it will work out.
In Europe, Molde had a good battle against Zenit in the Europa League-qualification, but lost in Russia and could not come back at home despite a 2-1 victory.
Solskjær is very much liked by both players and colleagues in Norwegian football.
He has a really good connection with the players, and are given much of the credit for helping Erling Braut Haland become one of history’s most expensive signings to leave Norway for Salzburg next month.
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