The Serie A side have confirmed the signing of Pereira as he joins on an initial season-long loan, with an option to make the move a permanent one next summer.
The Brazilian arrived in Rome on Thursday and posed with a club scarf in the airport, ahead of his medical and completing his departure from Old Trafford on Friday.
Solskjaer has confirmed that the arrival of Bruno Fernandes pushed Pereira out of the door.
"Yes, definitely. They're a big club, Lazio. Andreas needs to play regularly," the Norwegian told United's official site when asked if it was a good move for Pereira.
“He started last season really well and played loads of games. You could see the confidence growing and see him developing but, after we signed Bruno, that position that Andy played in was taken because Bruno came in and had such an impact. We decided this is what was best for Andreas."