Hurt's agent confirmed the actor's death, reported Variety.
No cause of death was immediately known, but Hurt revealed in 2015 that he was battling pancreatic cancer.
The actor first came to prominence after appearing in the best picture Oscar-winning "A Man of All Seasons" in 1966.
Hurt, who decided against a career as an art teacher to study at the Royal Academy of Dramatic Arts, appeared in countless TV and film roles, including roles in Michael Cimino's "Heaven's Gate," Stephen Frears' "The Hit," Sam Peckinpah's "The Osterman Weekend" and the 1984 adaptation of George Orwell's "Nineteen Eighty-Four," where Hurt played the novel's protagonist Winston Smith.
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Two years later, Hurt appeared in what was his greatest role as the anguished John Merrick in David Lynch's "The Elephant Man."
In recent years, Hurt appeared as Mr Ollivander, the wand-maker in the first Harry Potter film, "Harry Potter and the Sorceror's Stone," and for parts 1 and 2 of "Harry Potter and the Deathly Hallows," however his scenes in "Harry Potter and the Goblet of Fire" were cut.
Though he always prioritised film acting, Hurt also made regular appearances on stage, including the first West End production of David Halliwell's cult play "Little Malcolm" and His Struggle Against the Eunuchs in 1967.
Hurt also played numerous roles on TV, including Alan Clark in the 2004 adaptation of "The Alan Clark Diaries" and the "Doctor" in the 50th anniversary special episode of Doctor Who in 2013.
He was married four times, the first time to actress Annette Robertson in the early 1960s, the second time to Donna Peacock, the third time to Jo Dalton.
Many celebrities took to Twitter to express their condolences on Hurt's demise.
"It was terribly sad today to learn of John Hurt's passing. He was a truly magnificent talent," tweeted Mel Brooks.
Stephen Fry tweeted, "Oh no. What terrible news. We've lost #JohnHurt as great on the stage, small screen and big. A great man & great friend of Norfolk & #NCFC".
Chris Evans said, "John Hurt was one of the most powerful, giving, and effortlessly real actors I've ever worked with. Remarkable human being. U will be missed."
Elijah Wood tweeted, "Very sad to hear of John Hurt's passing. It was such an honor to have watched you work, sir.