The Portuguese forward signed from Manchester United in the summer of 2009 but is leaving for a "new step" at Juventus.
Real Madrid released a letter, penned by Ronaldo, on their website:
"These years in Madrid, and in this city of Madrid, have been possibly the happiest of my life.
"I only have feelings of enormous thanks for this club, this fanbase and this city. I can only give thanks to all of them for the love and affection that I have received.
"However, I think that the moment has arrived to start a new chapter in my life and therefore I have asked the club to accept letting me leave. I am sorry it is like this and I ask all of you, especially our followers, to please understand me.
"These have been nine absolutely marvellous years. These have been nine unique years. It has been an emotional time for me, full of consideration because Real Madrid takes the most out of you but I know very well that I won't be able to ever forget that here I've enjoyed football in a completely unique way.
"I have had on the field and in the dressing room some fabulous teammates, I have felt the heat of an incredible fanbase and together we have won three consecutive Champions Leagues and four in five years. Together with those I have the individual satisfaction of having won four Ballon d'Or and three Golden Boots. All during my spell in this immense, extraordinary club.
"Real Madrid has conquered my heart and that of my family, and that is why more than ever I want to say thanks: thanks to the club, to the president, to the directors, to my friends, to all the coaches, doctors, physios, incredible workers that make everything function that are attending tirelessly to every detail.
"Infinite thanks one more time to our fans and thank you also to Spanish football. During this incredible nine years I have played against incredible players. My respect and my recognition goes out to all them.
"I have reflected a lot and I know that the moment has arrived for a new cycle. I am leaving but this shirt, this badge and the Santiago Bernabeu I will continue to feel as something that is mine wherever I go.
"Thank you to everyone and, of course, like I said for the first time in our stadium nine years ago: Hala Madrid!"
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