Anderson believes the 29-year-old could be the man to help United regain the title.
The ex-England international told MUTV's Wednesday Night Phone-in: "I think he's a great acquisition, a fantastic and exciting signing.
"He's an established Premier League player. He can play out wide, off another forward or on his own up front, and he scores goals - 37 of them last season.
"I know he's 29 and you're not going to get the money back for him, but it's about the next couple of seasons. If we win the league and Champions League, it's money well spent.
Van Persie was linked with other clubs, including Manchester City, but Anderson is heartened that he opted for United.
"City would have paid anything to get him there, so it can't be about money," he reasoned. "He wants to play for United and be a part of the tradition of this club - and that says a lot."