Kagawa's Japan team-mates said the 23-year-old deserved his move to the English giants, while experts said the versatile attacking midfielder would be an important asset for United -- and not just for his marketing potential.
"Shinji deserves to be playing for a top club. He belongs," said fellow Japan international Keisuke Honda, who plays for CSKA Moscow. "I hope he does well."
Kagawa has caught the eye with 21 goals in 49 appearances over two seasons for Borussia Dortmund -- who won the German league and cup double this year -- as well as a hatful of assists.
The lively, right-sided player, who can play behind the main striker or on the left or right, and is also blessed with defensive awareness, is considered an important acquisition as United update their team.
The 19-time English champions lost their Premier League title to neighbours Manchester City this season, and floundered in Europe. Meanwhile old-stagers Paul Scholes, Ryan Giggs and Park Ji-Sung are in the twilight of their careers.
On Tuesday, United said they had agreed terms for Kagawa, pending a medical and visa clearance. The deal is expected to cost around ?12 million ($18.4 million), dwarfing the figure United paid for Park in 2005.
Fresh-faced Kagawa is now set to become the Premier League's biggest Asian signing and the most prominent player ever from Japan, eclipsing Hidetoshi Nakata who starred in Serie A a decade ago.
But he cut a reluctant figure when cornered by media in Saitama, where Japan are preparing to face Jordan on Friday.
"I haven't put pen to paper yet," Kagawa said, according to Kyodo news agency. "We still have two more games to play, and the entire team is focused on these qualifiers.
"I'll talk about all of this once I'm done here. I hope people will understand."
Asian newspapers splashed with the news on Wednesday, with Singapore's New Paper calling Kagawa the "real deal".
"What (Manchester United) need is a player who can change the pace of attack with ingenuity and accelerate the attack. That may be why they acquired Kagawa," said Japan's Nikkei business daily.
"Kagawa may well back up (striker Wayne) Rooney effectively. And he may well step up himself with the help of the sophisticated Rooney."
Press coverage in England was also positive, although the mass-market Daily Mail dubbed him "Shinji Kaga-who?" and said fans would be hoping for higher-profile signings.
However, few backed the theory that Kagawa had been brought in by United, recently rated as the world's most popular club, simply to sell shirts and merchandise in Asia.
"Kagawa meets the club's need to find a player who can feed decisive passes to England forward Rooney and organise their midfield," said a commentary in Japan's Asahi Shimbun newspaper.
"At present, Kagawa may be positioned as a 'quasi-regular'. But there is no doubt that Kagawa will be a type of player needed by Manchester United."
Team-mates were also in no doubt about Kagawa's ability to find his feet at Old Trafford, despite an indifferent season for Asian players in the Premier League.
"Kagawa can keep the ball in the smallest of spaces and is a quick decision-maker," Arsenal winger Ryo Miyaichi told Kyodo News. "He can play there (Manchester United) for sure.
"He's Japan's number 10, and I think he'll be able to perform even at a glamorous side like Manchester United."
Even for Japanese captain Makoto Hasebe, 28, Kagawa's move was the stuff of fiction and childhood day-dreams.
"For a player of my generation, moving to a big club is just a story in a manga comic," said Hasebe, who plays for VfL Wolfsburg in Germany. "I think children of today may feel like becoming another Shinji."