The Netherlands striker joined the Red Devils from Arsenal in a deal that could be worth £24 million in time to make his club debut as a substitute against Everton on Monday.
After Van Persie claimed that his heart was set on signing for United despite interest from Manchester City and Juventus, Giggs was delighted to see the club acquire a player so keen to play for the 19-time league champions.
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"I'm biased but players should want to come to United because you're always guaranteed to be up there challenging for trophies, there's a great team spirit, top facilities and you get to play for a great manager. There are so many plus points."
United were beaten 1-0 by Everton at Goodison Park in a disappointing start to the new campaign but Giggs has now turned his attention to the club's first home match of the season against Fulham.
Sir Alex Ferguson's team face the Cottagers looking to put their first points of 2012-13 on the board as they seek to take the title back from Manchester City.
"Your first home game is the one that the fans are always excited about," Giggs continued. "They want to see the team again and the new players.
"I'm more excited than ever about the season. You appreciate and try to enjoy things a lot more as your career comes towards the end and I'm no different. I can't wait for it all to unfold.
"It wasn't a nice feeling to lose the title last season – it never is, but it was the manner in which we lost it which was tough to take. I'm sure if we put that much effort in again and get that little bit of luck then we'll go that extra step."