“The player remains linked to the club during the next five seasons, until June 30, 2024,” said Real on its website.
Hazard’s transfer is subject to the Belgian international completing a medical and signing his contract with the Spanish club, said Chelsea.
“The memories he leaves us with will not fade. He provided all who watched Chelsea play with great entertainment and many match-winning contributions, and for that we thank Eden enormously.
“He has been a model professional throughout his time at the club, a wonderful individual to have around and a joy to work with. We look forward to welcoming him back to Stamford Bridge in the future.”
Hazard’s move to Real Madrid has been one of the most long-winded transfer sagas of the season.
“I think it’s a goodbye but in football you never know,” said the Belgian international.
“We will decide in a few days – the only target in my mind was to win this final. Maybe now it is the time for a new challenge.
“My dream was to play in the Premier League and I have done that for one of the biggest clubs.”
Earlier on Friday, Chelsea launched an appeal to Switzerland’s Court of Arbitration for Sport over FIFA’s transfer ban.