The Norwegian fills the void left after Jose Mourinho was sacked on Tuesday morning and will take charge at Old Trafford until the end of the season.
The 45-year-old has had one spell in charge of a Premier League side before, when he managed Cardiff in 2014.
Solskjaer took over at the Welsh side on 2 January 2014 after the departure of Malky Mackay, although it was not exactly a successful stint.
The former Norway international took charge of 18 Premier League games as Cardiff manager, winning three, drawing three and losing 12 of them.
In that time the Welsh side scored 17 goals and conceded 42, eventually finishing bottom of the table with 30 points from 38 games.
After relegation, Solskjaer continued in the job, leading Cardiff into the 2014-15 Championship season.
However, after a bright start, which saw the team pick up seven points from their first three games, their form tailed off.
Three defeats in four league games, including back-to-back home losses to Norwich and Middlesbrough were enough to get Solskjaer fired on 18 September 2014.
Ole Gunnars overall recored at Cardiff, including cup games, was nine wins, five draws and 16 defeats in 30 games.
That left him with a win ratio of 30%.
Solskjaer played for Manchester United from 1996-2007 and told the clubs official website: Manchester United is in my heart and its brilliant to be coming back in this role.
Im really looking forward to working with the very talented squad we have, the staff and everyone at the club.