Hazard, 32, joined Madrid from Chelsea in July 2019 as one of the Premier League's biggest stars, signing a five-year deal in a move worth an initial €100 million.
His four seasons at the Santiago Bernabeu have been marred by persistent injury problems, and he has made just six LaLiga appearances this season -- four of them as a substitute -- scoring no goals.
"Real Madrid C.F. and Eden Hazard have reached an agreement whereby the player will be released from the club as of June 30, 2023," Madrid said in a statement on Saturday.
"Eden Hazard has been part of our club for four seasons, in which he has won eight trophies: one European Cup, one Club World Cup, one European Super Cup, two Leagues, one Copa del Rey and two Spanish Super Cups.
"Real Madrid wants to express its affection for Eden Hazard and wishes him and his entire family the best of luck in this new period."
Hazard's injury problems began during his first season in Madrid, with an ankle fracture requiring surgery and the insertion of a metal plate, which caused further problems before being removed two years later.
He retired from international football in December, after Belgium's group stage exit at the 2022 World Cup.
A month earlier, Hazard had apologised to Real Madrid fans in an interview with the newspaper Marca, saying he was "really sorry about what has happened" and rating his impact on the field as "zero," saying he would accept a move this summer.