According to press reports in the United Kingdom, the 28-year-old, who had one year left on his contract with the London based club could cost Real Madrid a total of 130 million pounds (165 million USA dollars) including bonus payments.
Hazard scored 16 Premier League goals and provided 15 assists as Chelsea finished third in the standings, then providing a fitting swansong with two goals and an assist in the 4-1 win over Arsenal in the Europa League final.
Chelsea director Marina Granovskaia said: "The memories he leaves us with will not fade".
Eden Hazard who is a Belgian Professional footballer, will be now known as a former player of Chelsea Football club. However, football to me is about having a ball at my feet, playing games and enjoying every moment, we are lucky to play the attractive game and this is always my advice to those who ask for a coaching tip!
It was believed that the Premier League side wanted closer to £115m for Hazard, but it seems they have chose to sell for less.
Hazard will join Serbian striker Luka Jovic, Brazilian defender Eder Militao and forward Rodrygo Goes as Real's new signings in what promises to be a busy summer at the Santiago Bernabeu.
Chelsea has paid tribute to Hazard, who joined from French side Lille in 2012.
During some form of live stream for Chelsea TV, Hazard outright called five-time Ballon d'Or victor Leo Messi the best player in the world without any hesitation.
The famous "Garden of Eden" banner which has hung at the Shed End of Chelsea's stadium throughout the forward's career will be taken down as the club enter the post-Hazard era. but it could one day make a return.
Chelsea had just won the Champions League when Hazard chose them over several other clubs but they have failed to replicate the success in the competition.
Where will Hazard fit in at Real Madrid? . The 13-time Champions League winners mean serious business in this summer's transfer window as they also look to sign Lyon left-back Ferland Mendy and Tottenham Hotspur midfielder Christian Eriksen in the coming weeks.