The actor was a star of the golden era of French cinema, known for his tough-guy persona on screen in hits including The Samurai and Borsalino.
"He passed away peacefully in his home in Douchy, surrounded by his three children and his family," a statement released to AFP news agency said.
Delon has been in poor health in recent years and become a virtual recluse. More recently, the breakdown of his family had been making headlines in France.
Once described as the most beautiful man in the movies, Delon starred in hits from the 1960s including The Leopard and Rocco and his Brothers.
From the 1990s, his film appearances grew rare, but he remained a fixture in the celebrity columns.
In total, he appeared in more than 90 films during the course of his career.
A statement from his family said: "Alain Fabien, Anouchka, Anthony, as well as (his dog) Loubo, are deeply saddened to announce the passing of their father.
"He passed away peacefully in his home in Douchy, surrounded by his three children and his family."
Le Parisian newspaper called Delon “a legend of the cinema”, while Liberation described him as “a leading figure of cinema, symbol of shadowy masculinity, the actor with crazy charisma”.
Delon's last major public appearance was to receive an honorary Palme d'or at the Cannes film festival in May 2019.
At the event, he made an emotional speech in which he appeared to bid farewell to cinema.
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