Van Persie left Arsenal for United last night.
Vialli told the Mirror: "It [is] a massive signing. Van Persie and (Wayne) Rooney combining in the same team makes for a pretty exciting striking partnership.
"It will be a very important addition to an already very strong team.
"If you can't extend a player's contract then you need to do what's best for the club.
"But you might also want to do what's best for the player.
"If the player has been working and has been behaving professionally for you for a number of years, then I think it's only right you try to do what is right for the player as well."