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Hazard, 32, joined Real from Chelsea in 2019 for a fee of 115 million euros ($123 million) and was presented to up to 50,000 supporters at the Santiago Bernabeu.
The Belgium international was on top of his game, scoring twice in his final match with Chelsea to help the English club win the Europa League by beating Arsenal 4-1.
But almost immediately the player voted Premier League player of the season in the 2014-2015 campaign was hampered by injuries to his ankle in Spain.
He made just 54 league appearances, including six this season, and scored seven goals.
"Real Madrid Football Club and Eden Hazard have reached an agreement whereby the player will leave the club as of 30 June 2023," Real said in a statement.
"Real Madrid would like to express our affection to Eden Hazard and we wish him and his family the best of luck for the next stage of his career."
Forward Marco Asensio said on Saturday he was also leaving Real Madrid at the end of his contract in June.
Asensio won La Liga and the Champions League three times each with Madrid, as well as the Copa del Rey this season for the first time, scoring 61 goals in 285 appearances.
The forward offered an explosive impact from the bench but never managed to establish himself as a key starter for Los Blancos.