The signing of the latest Ballon d'Or victor and top scorer in the Champions League for the last six seasons represents a major coup for Juve, who have had a stranglehold on the Italian title since 2012 but have not won Europe's top prize since 1996.
In a statement the Spanish giants said: "Real Madrid would like to place on record its thanks to a player who has shown himself to be the best in the world and made his mark on one of the greatest periods in our club's history and on the world game".
"If he doesn't leave, we still have him for his best moments". After the deal, Cristiano Ronaldo wrote an official letter to Real Madrid fans saying he only has feelings of enormous gratitude for Real Madrid club and the city.
The Portuguese won the Champions League on four occasions too, La Liga twice, and the Copa Del Rey twice.
The two clubs reached a deal reportedly worth 112 million euros (about US$132 million).
Zidane's presence was thought to be a major draw for Hazard, but the Frenchman stepped down from his role just days after guiding the club to a third successive Champions League trophy last season. My respect and recognition to them all.
Madrid have tended to get their way in the transfer window in recent years, as they have the financial muscle and pulling power to get the players they want.
How do you think Real will replace Ronaldo?
The Portuguese laughed off Milan's attempts to lure him to Italy a few years ago, but now he has chose to chance his arm in Serie A.
"They look like they are looking at other positions".