Kagawa completed his move from German double winners Borussia Dortmund on Friday after passing a medical.
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.
And, after missing out on Lille's Eden Hazard, the United boss is delighted to have got his man.
"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."
Kagawa is United's second capture of the summer, following the arrival of England Under-19 international Nick Powell from Crewe.
Ferguson has been under pressure to strengthen his midfield for two years now, with many fans believing it lacks quality compared to a number of United's rivals.
Paul Scholes did abandon his retirement in the middle of last season and, together with Ryan Giggs, has signed on for a further year with the Red Devils.
However, with question marks over the fitness of Anderson and Darren Fletcher, who is still to attempt a comeback after it was revealed he was suffering a bowel complaint, Ferguson had to make a move.
Reports that Luka Modric will demand a summer move away from Tottenham are bound to be of interest to Ferguson, although he would face stiff competition from Real Madrid for the Croatia star.
Kagawa does bring some impressive statistics to United, though, 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.
For that reason alone, he should also avoid claims of being little more than a signing to sell shirts, a label that was attached to Park Ji-sung for so long.
"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."