Borussia Dortmund and Kagawa have agreed terms with United and the player only needs to pass a medical and obtain a work permit to become manager Alex Ferguson's first big signing of the close season.
The Japanese midfield playmaker, playing in a more advanced role, has been in superb form for his country in their three recent World Cup qualifiers, scoring once and providing numerous assists to leave Japan top of their pool.
He can also play down the left, but Kagawa is eyeing a more central role at United, who narrowly lost out on the title to Manchester City in May.
"I want to play (in the hole)," Kagawa told the Kyodo news agency on Wednesday. "I feel like that's where I play my best football. I plan on working hard so I can win my place at the position.
"They're one of the biggest clubs in the world, and I was given a chance to play for them. I took a lot of things into consideration, like the fact that they've got a deep squad, their style of football and it wasn't an easy decision.
"But I wanted the challenge."
United have been linked with numerous central midfielders in recent seasons to help complement the attacking threat they pose down the flanks with Nani, Ashley Young and Antonio Valencia.
Despite being strongly linked with Inter Milan's Wesley Sneijder and Tottenham Hotspur's Luka Modric, United failed to sign anyone and tempted Paul Scholes out of retirement to fill the role last season.
Kagawa said that once he had heard of United's interest, the chance to join the English Premier League was too good to turn down.
"When you look at the football scene, it's the best league in the world. You've got the world's biggest clubs like (Manchester) City, Arsenal, Liverpool, Chelsea all in the same league which is fascinating.
"In the Bundesliga, the only games that compare are the ones against Bayern (Munich). I feel like I'd be able to gain so much by playing big games on a regular basis, including the Champions League. I can't help but be excited."
Kagawa had been linked with other clubs but the chance to work with Ferguson was appealing, the 23-year-old who scored 21 goals in 49 league games in Germany, explained.
"There was some talking going on with other clubs, but Manchester were the first to make me a formal offer and the more I talked to them, the more I felt Manchester was the place for me to be.
"I met (Ferguson) and contacted him a few times afterwards. I thought we hit it off, which meant a lot to me. He told me, 'Don't worry about a thing, trust me. I would love it if you could take on this huge challenge'."
"And when a legendary man like him says that to you, it carries a lot of weight."