"Cristiano has been a marvellous player for Manchester United," he said.
"His six years at Old Trafford have seen him develop into the best footballer in the world."
"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."
Ronaldo was on holiday in the United States at the time the offer was made by Real on 10 June.
During that time, United stated that the decision came at the Portugal international's request after he "again expressed his desire to leave".
The addition of Ronaldo to the Real ranks is part of a remarkable spending spree by the Spanish giants since Florentino Perez returned as club president on 1 June.
He brought in Brazil playmaker Kaka for a then world record £56m, Ronaldo was then lined up for £80m before centre-back Raul Albiol was signed from Valencia for £12m, to bring Real's total summer spend, so far, to £148m.
Perez appointed Villarreal boss Manuel Pellegrini as Real's new coach and had previously made it clear he would do "everything possible" to sign Ronaldo.
Reports have suggested that the midfielder will earn about £11m per year, which will make him the highest paid footballer in the world. He was on about £6.38m at Old Trafford.
Ronaldo spent six years at Old Trafford
The current top earner in the world is understood to be Inter Milan striker Zlatan Ibrahimovic, who is on about £10m per year.
Despite the vast outgoings, Real have also been linked with Liverpool's Xabi Alonso, Valencia's David Villa and Bayern Munich's Franck Ribery.
Ronaldo joined United in 2003 from Sporting Lisbon for £12.2m but was strongly linked with a move to the Spanish capital in the summer of 2008.
United lodged a complaint with world governing body Fifa in June 2008 over what they believed was a deliberate attempt by Real to unsettle the player.
After a long, drawn-out saga that ran through the summer months, Ronaldo insisted he was happy at Old Trafford and remained at United for the 2008-2009 campaign.
But despite Ronaldo's claim that he wanted to remain at Old Trafford, he was the subject of constant speculation last season and often issued mixed messages about his future.
It took time for Ronaldo to find his best form after arriving in England but he became a pivotal player for United, who have won the last three Premier League titles.
In 2007-08, he scored 42 goals, which topped the previous club record for a midfielder held by George Best and was on the scoresheet as United defeated Chelsea in the Champions League final.
His form through 2008 resulted in him being named Fifa World Player of the Year in January - only a month after he won the Ballon d'Or as the European Player of the Year.
Ronaldo was the top scorer for his club last season, with 26 goals, taking his total for United to 118 in 292 appearances.
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