The Oscar-nominated star was well known for roles including Quentin Crisp in The Naked Civil Servant, the title role in The Elephant Man and wand merchant Mr Ollivander in the Harry Potter films.
His agent, Charles McDonald, confirmed his death to the Press Association on Saturday.
The British actor was nominated for two Academy Awards, for The Elephant Man and Midnight Express, and won four Bafta Awards, including a lifetime achievement recognition for his outstanding contribution to British cinema in 2012.
Hollywood legend Mel Brooks described him as “a truly magnificent talent”.
“No one could have played The Elephant Man more memorably. He carried that film into cinematic immortality. He will be sorely missed,” he added.
Stephen Fry celebrated the “great man” for excelling as an actor, whether he was working in cinema, television or on the stage.
Richard E Grant tweeted: “So so sad to have lost such an extraordinary talent and friend. Sir John Hurt. R. I. P.”
Sir John told the Press Association of his diagnosis in June 2015.
He said: ‘’I have always been open about the way in which I conduct my life and in that spirit I would like to make a statement.
‘’I have recently been diagnosed with early stage pancreatic cancer. I am undergoing treatment and am more than optimistic about a satisfactory outcome, as indeed is the medical team.
‘’I am continuing to focus on my professional commitments and will shortly be recording Jeffrey Bernard Is Unwell (one of life’s small ironies!) for BBC Radio 4.’’
He later told the Radio Times: “I can’t say I worry about mortality, but it’s impossible to get to my age and not have a little contemplation of it.
“We’re all just passing time, and occupy our chair very briefly. But my treatment is going terrifically well, so I’m optimistic.”
Sir John enjoyed a big hit with sci-fi horror Alien in 1979 and his character’s final scene has been frequently named as one of the most memorable in cinematic history.
He recently found new fans when he starred as a “forgotten” incarnation of the Doctor, known as the War Doctor, in Doctor Who.
He was knighted by the Queen for services to drama at an investiture ceremony at Windsor Castle in 2015.
Earlier this year Sir John pulled out of a production of John Osborne’s play The Entertainer on medical advice, as he recovered from an intestinal complaint.
He had been due to play Billy Rice in the Kenneth Branagh Theatre Company production, directed by Rob Ashford.
However, he continued to work at a prodigious rate, starring in Jackie Kennedy biopic Jackie, thriller Damascus Cover and the upcoming biopic of boxer Lenny McLean, My Name Is Lenny.
He was also filming Darkest Hour, in which he starred as Neville Chamberlain opposite Gary Oldman’s Winston Churchill.
The film focuses on Churchill’s charge against Adolf Hitler’s army in the early days of the Second World War and is due to be released on December 29.
Sir John, who played Caligula in the celebrated BBC drama I, Claudius, also racked up film hits in V for Vendetta, Indiana Jones and the Kingdom of the Crystal Skull, Tinker Tailor Soldier Spy and Hercules.
Other celebrated roles included his performance as Stephen Ward - a key figure in the Profumo affair - in Scandal and a reprisal of his role as Crisp for An Englishman In New York in 2009, 34 years after his original portrayal of the flamboyant figure.
Sir John’s distinctive voice has been used several times as narrator, and accompanied a chilling Aids awareness advertising campaign in the 1980s.
Born in Chesterfield, Derbyshire, Sir John went to art college before he studied at Rada (Royal Academy of Dramatic Art) and picked up TV and film roles until he had his major breakthrough, appearing in A Man For All Seasons as Richard Rich.
Sir John achieved further prominence in the film 10 Rillington Place as Timothy Evans who was wrongly executed for the crimes of serial killer John Christie, played by Richard Attenborough.