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6 year oldIt is understood a deal worth £105m has been reached between the two clubs that will see the 33-year-old Portuguese end a nine-year stay at the Bernabeu.
Ronaldo won four Champions Leagues and two La Liga titles at Real.
"The time has come to open a new stage in my life, that's why I asked the club to accept transferring me," he said.
Ronaldo joined Real from Manchester United for £80m in July 2009 and scored a club-record 451 goals and won the Ballon D'Or - awarded to the world's best footballer - in 2008, 2013, 2014, 2016 and 2017.
He has helped them win the Champions League in four of the past five seasons, scoring in the 2014 and 2017 finals.
"For Real Madrid Cristiano Ronaldo will always be one of its great symbols," said a club statement.
"Real Madrid wants to express its gratitude to a player who has proved to be the best in the world and who has marked one of the brightest times in the history of our club and world football.
"Real Madrid will always be your home."
He is now set to be unveiled as the Italian club's record signing, eclipsing the £75.3m they paid for Gonzalo Higuain.
Despite their dominance in Europe's premier club competition, Real struggled domestically, finishing 17 points behind champions Barcelona last season.
Real are keen on reshaping their team under new manager Julen Lopetegui and the 33-time La Liga winners have also been linked with a move for Paris St-Germain's 26-year-old Brazil forward Neymar.
However, it would be a controversial move as Neymar spent four years at Real's fierce rivals Barcelona before joining Paris St-Germain in a world record transfer of £200m last summer.
Real have also been linked with a move for another PSG forward, Kylian Mbappe, the 19-year-old who has helped France reach the semi-finals of the World Cup.
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