The novelist – best known for his popular 1986 tale about a slow-witted but kind-hearted man from Alabama – died on Wednesday.
News of his death was confirmed by Mayor Karin Wilson of Fairhope, Alabama, who said in a message on social media that he had died in the south Alabama town.
According to the Associated Press, a local funeral home also confirmed the death and said arrangements were pending.
His cause of death is not yet known.
Winston’s Forrest Gump was adapted into a 1994 blockbuster film starring Tom Hanks in the lead role.
It grossed more than $683 million (about £527 million) at the global box office, as well as winning six Academy Awards, including Best Picture and Best Actor for Tom Hanks.
Following the success of Forrest Gump, Winston wrote a follow-up, 1995’s Gump and Co.
Winston graduated from the University of Alabama in 1965 before a spell in the US Army, which included a tour of duty in the Vietnam War.
He was also a former journalist, also wrote non-fiction on a range of subjects, including the American Civil War.
Alabama governor Kay Ivey was among those who paid tribute, writing on Twitter: “Saddened to learn that Alabama has lost one of our most gifted writers.
“While he will be remembered for creating Forrest Gump, Winston Groom was a talented journalist & noted author of American history. Our hearts & prayers are extended to his family.”