The 23-year-old netted 13 goals in 31 appearances as Dortmund won the Bundesliga title and German Cup last season, taking his tally to 29 goals since joining from Cerezo Osaka in 2010.
The United manager revealed the 19-time champions had been tracking the midfielder for a number of seasons, and Ferguson is convinced Kagawa, who was named man of the match in the Red Devils’ opening pre-season friendly in China, can be a success at Old Trafford.
“There was a lot of interest in him after his first season because he started so well at Dortmund,” Ferguson told United’s website.
“But I never think you can tell after one season. I wanted to see how he’d do in his second campaign – it’s more of a test because your opponents tend to know more about you.
“He passed with flying colours. He was even better, in fact. So that was a straightforward decision for us.”
“Shinji’s intelligent, fast, has quick feet and works very hard. At 23 he’s a good age and already has a couple of years’ experience at a big club in Borussia Dortmund.
“It’s obvious he’s a very good player. We have high hopes for him.”
Kagawa expressed his delight at scoring for United, but the Japanese playmaker refused to get carried away, and eyed upcoming fixtures as a chance to prove his ability.
“I’m happy that I scored, but we weren’t playing against a top opponent,” Kagawa said. “Once our internationals return, I’ll be able to play at a higher level.”