Van Persie scored five goals in eight games in the competition last season as Arsenal reached the quarter-final stage.
Kagawa is less experienced in Europe's premier competition but did play six times last season as Borussia Dortmund were knocked out of the competition at the group stage, and Giggs believe his quality on and off the ball will stand him in good stead.
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"Robin has the experience of playing in Europe with Arsenal," Giggs told reporters. "The goals he has got will hopefully give us that extra edge this season.
"Shinji Kagawa is that kind of player who will thrive in Europe, where possession is key. He keeps the ball and gets into positions where he is hard to pick up.
"I am sure they will both be very good additions in Europe for us."
United failed to reach the knockout stage of the competition last season after falling to an away defeat to Basel in their final group match.
Giggs highlighted the Red Devils' home form prior to that game as costly, with Sir Alex Ferguson's team dropping points against both the Swiss side and Benfica.
"We need to win our home games," he acknowledged. "Usually 10 or more points gets you through, which means winning at home and trying to draw away.
"We didn't manage it last year because we didn't perform at Old Trafford the way we have done in the past."