The Japanese midfielder arrives with a big reputation from Borussia Dortmund.
Neville told manutd.com: "I'm really excited about watching him play and seeing how he fits in with the other talented players in this squad. He's had a fantastic couple of seasons at Dortmund, who have been magnificent in Germany.
"It's not easy to knock Bayern Munich off their perch. And if you look at the performances, Kagawa has played a big part in that.
"He might be one of these lads that comes to United and sneaks under the radar a little bit. He's not what you'd class as one of Europe's stellar names at the moment. But he could be somebody who has the same sort of impact as Chicharito or Ole Gunnar Solskjaer and go on to become a real sensation for United."