“Real Madrid would like to show its gratitude and affection to a player who is already one of our greatest legends.
“Karim Benzema’s career at Real Madrid has been a shining example of conduct and professionalism, and he has represented the values of our club. Karim Benzema has earned the right to decide his future.
“Madridistas and all the fans around the world have enjoyed his magical and unique football, which has made him one of the great icons of our club and one of the great legends of world football.
“Real Madrid is and will always be his home, and we wish him and all his family the best in this new stage of his life.”
Benzema, the current Ballon d’Or and UEFA Player of the Year, joined Real from Lyon in July 2009 for a reported transfer fee of 35 million euros.
He is fifth on the list of players with the most Real appearances and his trophy haul in Spain includes five Champions Leagues, five Club World Cups, four European Super Cups, four LaLiga titles, three Copas del Rey and four Spanish Super Cups.
Benzema has been linked with a move to Saudi Arabian side Al-Ittihad.
Real have confirmed they will hold “an institutional act of tribute and farewell” to Benzema in the Spanish capital on Tuesday in the presence of club president Florentino Perez.