The 29-year-old Dutch international completed a four-year deal worth £24m on Friday.
"It's a complete game-changer. An absolute game-changer," Schmeichel told talkSPORT.
"We have to go out there and perform and produce the results but, with a player like that in the squad, everybody is going to get a lift from that and everybody is going to up their game.
"It is one player that everybody in the world that have ambitions in football have been trying to sign. He came to us and I'm very, very happy."
Van Persie is expected to make his debut for United in their Premier League opener at Everton on Monday night.