Solskjaer, 45, made more than 360 appearances in 11 years for United and scored a dramatic Champions League winner in 1999 to seal a historic treble.
"It feels like coming home. It's been a few whirlwind days, very hectic," he said in his first interview since taking over from Jose Mourinho.
United called time on Mourinho's two-and-a-half years at the club on Tuesday, with the club languishing sixth in the Premier League, 19 points behind leaders Liverpool.
Solskjaer will be at the helm at Old Trafford until the end of the season, when the club will appoint a full-time successor.
Tottenham head coach Mauricio Pochettino is the current front-runner.
"It's six months, I'm going to enjoy the ride. It's about being myself. The club's running a process to find the next manager so I'm just going to be myself in the meantime," he added.
He will take charge of his first match on Saturday against Cardiff, where he spent an unhappy spell as manager in 2014.