The Belgian superstar finally arrives at the Bernabeu after years of being linked with Los Blancos.
Hazard will initially cost the Spanish giants around £88.5m (€100m) and is viewed as the man to fill the void left by Cristiano Ronaldo.
Los Blancos released the following statement on their website: "Real Madrid CF and Chelsea FC have agreed to the transfer of the player Eden Hazard.
"The player remains linked to the club during the next five seasons, until June 30, 2024.
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Hazard finally completes the move
"Eden Hazard will be presented as a new player of Real Madrid on Thursday June 13 at the Santiago Bernabéu stadium, after passing the relevant medical examination."
The 28-year-old was in the final year of his contract with Chelsea, with the Europa League final win over Arsenal in Baku his final game with the club.
Hazard scored 16 goals and assisted 15 more in his 37 Premier League appearances last season.
Busy summer at Real Madrid
The Telegraph report that the fee for Hazard could go as high as £130m, meaning Chelsea may have nearly made a £100m profit on the £32m they paid Lille for him in 2012.
Not bad for a player who could have left for free next summer...
With Hazard and Luka Jovic now signed and ready to go for 2019/20, Real have one of Europe's most exciting forward lines once again.
Zinedine Zidane's side have also brought in Brazilian duo Eder Militao and Rodrygo this summer as they begin their squad overhaul after a disappointing 2018/19.
The likes of Christian Eriksen, Paul Pogba and Ferland Mendy are just some of the other high-profile names being linked with moves to the world's most famous club.
The Blues paid tribute to the departing Hazard, too, writing in their statement: "Hazard leaves Chelsea as one of the great players in our history.
"He helped the team win the Premier League on two occasions, the Europa League twice and the FA Cup and League Cup once. He has been voted Chelsea Player of the Year on a record four occasions.
"A shining star throughout the many successes the team achieved, Hazard played 352 games for the club, the 23rd highest total in our history, and scored 110 goals, the ninth most.
"Chelsea Football Club wishes Eden well as we say a fond goodbye."
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