The Spanish giant confirmed the signing of the Belgium star on a five-year deal.
Hazard has been a long-term target for Madrid and hinted after last year's World Cup he planned to leave Chelsea.
But the 28 year-old stayed at Stamford Bridge for another season, helping them to Europa League glory with a brace in the 4-1 final victory over Arsenal in Baku.
Madrid also reveals the kit Hazard will wear
After that game, he again suggested he had played his final game for Chelsea and that has proved to be correct.
The former Lille star helped Chelsea win two Premier League and Europa League titles, as well as an EFL Cup and FA Cup during his seven years with the Blues.
He joins Madrid as part of Zinedine Zidane's squad overhaul that has already seen Rodrygo Goes, Eder Militao and Luka Jovic move to the Santiago Bernabeu.