The Spanish giants are understood to have struck a deal that could rise to a club-record transfer once all bonus payments are taken into account.
After months of speculation, the 28-year-old Belgian striker will be officially unveiled on June 13, once he has undergone his medical.
Shortly after the transfer was confirmed, he posted a 700-word goodbye to Chelsea supporters on his Facebook page, explaining that it was his dream to play for Madrid since he was a young boy and leaving Chelsea was "the biggest and toughest decision in my career to date".
The fee is reported to be in excess of £130 million (AED 600 million) which will make him the most expensive transfer ever involving an English club, overtaking the £106.4 million Barcelona paid Liverpool for Philippe Coutinho in 2018.
To my Chelsea friends and family, You now know that I will be joining Real Madrid. It’s no secret that it was my dream...Posted by Eden Hazard on Friday, June 7, 2019