"Cristiano has been a marvellous player for Manchester United. His six years at Old Trafford have seen him develop into the best footballer in the world," Ferguson told the Premier League club's website.
"His contribution has been a major factor in the club's success in that time and his talent, his ability to entertain and his infectious personality have enthralled fans the world over."
The World Footballer of the Year signed a six-year deal with Real under an 80 million pound transfer, the third signing in Real President Florentino Perez's "spectacular sporting project."
Perez spent around 67 million euros on AC Milan's Brazilian playmaker Kaka and also signed Spain defender Raul Albiol from Valencia for a reported fee of 15 million euros.
"Everyone here wishes him well in his future career," Ferguson added.
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