The Body Heat and Kiss Of The Spider Woman star’s son told fans on social media of his father’s death, which he said was from natural causes.
He said: “It is with great sadness that the Hurt family mourns the passing of William Hurt, beloved father and Oscar winning actor. He died peacefully, among family.
“The family requests privacy at this time.”
The US star was renowned for his Oscarwinning performance in 1985’s Kiss Of The Spider Woman.
He was also nominated for a best supporting actor Oscar for A History Of Violence and received a best actor nod for Broadcast News and Children Of A Lesser God.
More recently, Hurt also starred as General Thaddeus Ross in 2008 film The Incredible Hulk, before taking roles in Captain America: Civil War, Avengers: Infinity War, Avengers: Endgame and Black Widow.
During his time at performing arts centre The Juilliard School in New York, he took on the lead role in the 1980 film Altered States. It set him on the road to fame.
Hurt was also famous for films such as Body Heat in 1981 and Gorky Park in 1983.
He was married to American actress Mary Beth Hurt from 1971 to 1982, but they had no children.
He had one child with partner Sandra Jennings, two with Heidi Henderson – to whom he was married from 1989 to 1993 – and one with the French actress Sandrine Bonnaire.