Park enhanced his reputation as a national hero in South Korea when he moved to Old Trafford from PSV Eindhoven seven years ago.
Kagawa is joining from Borussia Dortmund to become the club's first Japanese player and Park is confident he will successfully make the transition.
"I know United have agreed a deal for Kagawa and I'm happy because we're signing a good player," Park told ManUtd.kr at an event hosted by his JS Foundation.
"Manchester United is a huge club and every season we sign new, world-class names.
"I hope Kagawa shows how good he is next season and I think he will do."
United have also signed Nick Powell from Crewe but Park welcomed the forthcoming battle for midfield places.
"There is a lot of competition in the squad but it doesn't matter who I'm competing with," he added.
"We're a team and I just want to concentrate on producing better performances.
"We're starting our pre-season tour next month and those matches will help me to prepare for the new season.
"As always, when I begin a new season I am determined to improve."
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