An "unconditional 80 million pounds" fee was agreed between the clubs last month and then last Friday the Spanish giants announced that the signing of the world player of the year was official.
A statement on the Manchester United club website on Wednesday confirmed that the transfer fee had been paid.
Manager Sir Alex Ferguson used the occasion to pay tribute to the Portuguese winger despite friction between him and the player last season as the Real transfer loomed.
"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," he said.
"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.
"Everyone here wishes him well in his future career."
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