Kagawa completed his move from German double winners Borussia Dortmund after passing a medical on Friday.
The Japan midfielder has signed a four-year contract and is expected to accompany United on their pre-season tour of South Africa and China after it was confirmed he would not be selected for Olympic duty. Ferguson said: "Shinji is an exciting young midfielder with great skill, vision and a good eye for goal."
He added: "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."
Kagawa brings some impressive statistics to United as he looks to help the Red Devils reclaim the Premier League title. He helped Dortmund land successive German titles and scored 17 times in addition to claiming 13 assists as they also went on to complete the double last term.
"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."