The 23-year-old passed a medical on Friday prior to the deal being finalised the deal that could cost United up to £17 million although he is yet to be granted a work permit.
Kagawa’s enjoyed a stunning two year-spell in the Bundesliga winning back-to-back titles including the double last season in which he scored 17 times in addition to claiming 13 assists.
After announcing the signing Ferguson enthused over the Japanese international and hopes he can make an immediate impact as they aim to wrestle the Premier League trophy back from rivals Manchester City next season.
“Shinji is an exciting young midfielder with great skill, vision and a good eye for goal,” said Ferguson.
“I am delighted he has chosen to come to United.
“I believe he will make an impact upon the team very quickly as he is suited to United’s style of play.
“We are all looking forward to working with him.”
Having missed out on Lille star Eden Hazard to Chelsea the signing of Kagawa will have come as somewhat of a relief to the Red Devil’s support and Ferguson, particular, as it looks to have ended his search for Paul Scholes’ long-term replacement.
Reports have suggested that the he was bought purely to sell shirts in Asia, a tag that stuck with Park Ji-sung for song long, but the midfielder insists he can’t wait to get started at United.
“This is a challenge I am really looking forward to,” said Kagawa.
“The Premier League is the best league in the world and Manchester United is such a massive club.
“This is a really exciting time for me. I can’t wait to meet the team and start playing.”