Ward - who starred in The Right Stuff, Short Cuts and Tremors - died last weekend, his representative told the New York Post.
No cause of death has been anounced, as per his family wishes, it has been reported.
A statement to the US publication said: “I am sad to announce the passing of acclaimed actor Fred Ward, who passed away on Sunday, May 8, 2022 at age 79.”
The late star’s representative Ron Hofmann asked any memorial tributes were made in the form of donations to the Boston University Chronic Traumatic Encephalopathy Center.
Mr Hofmann added Ward spent the last years of his life developing “his second favorite art form: painting”.
Ward, who was born in San Diego, began his acting career in 1979, starring alongside Clint Eastwood as his jailbreak buddy John Anglin in Escape from Alcatraz.
He took on another major role in 1983 when he starred as astronaut Gus Grissom in the historical film The Right Stuff, alongside Ed Harris and Dennis Quaid.
Ward is also known for his roles in Tremors, and its sequel Tremors 2: Aftershocks, as well as The Right Stuff, Remo Williams: The Adventure Begins and Miami Blues.
Tributes have begun to pour in for the late actor, with Rolling Stone editor Alan Sepinwall hailing Ward’s “great, lived-in performances”.
He wrote on Twitter: “RIP, Fred Ward, a great character actor whose big shot at leading man status, Remo Williams: The Adventure Begins, unfortunately flopped, but who kept giving great, lived-in performances for the rest of his career”.
Ward is survived by his wife of 27 years, Marie-France Ward, and his son Django Ward.