Van Persie's appearance off the bench in Saturday's 4-0 Barclays Premier League win over Wigan showed the Dutchman has no lingering effects from the groin injury that curtailed his international involvement.
It also confirmed manager Sir Alex Ferguson's determination not to take any chances in Europe this term after admitting he got his team selections badly wrong last season, when United went crashing out in the group stage. "Robin has the experience of playing in Europe with Arsenal," the 38-year-old Welshman said.
And with fellow summer signing Kagawa also set to return after being given additional time to recover from his arduous trip to Japan, Giggs is expecting both men to make a positive impact.
Ahead of Wednesday night's opener with Turkish outfit Galatasaray, Giggs added: "The goals he has got will hopefully give us that extra edge this season. Shinji 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."
After reaching three finals in the previous four seasons, United's early exit last term came as a shattering blow. The Red Devils gleaned just two victories - back-to-back triumphs against Romanian minnows Otelul Galati.
They threw away a two-goal lead against Basle on home soil, and were then beaten in their final match in Switzerland when they only needed a point to advance.
Ferguson will demand there is no repeat this time around. And Giggs believes he knows just how to do it.
"We need to win our home games," he said. "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."