Kagawa had a whistle-stop medical at United before returning home to Tokyo yesterday.
"I've just joined the team and haven't accomplished anything yet.
"I want to make a name for myself [at United] on my own terms.
"The contract was as long as I'd expected from a club [like United]," Kagawa laughed. "When I was at [Old Trafford], I thought about how incredible it would be if I could score there."