The Scottish Bafta-winning star played the British spy in seven films from 1962 until 1983.
He died in his sleep in the Bahamas.
While the cause of death is yet to be announced, it is believed the actor had been unwell for a long period of time.
Connery’s son, Jason, said his father "had many of his family around him" when he died in Nassau.
"We are all working at understanding this huge event as it only happened so recently, even though my dad has been unwell for some time."
Jason added: "A sad day for all who knew and loved my dad and a sad loss for all people around the world who enjoyed the wonderful gift he had as an actor."
Connery’s first appearance as 007 came in Dr No in 1962. His other Bond films included From Russia with Love (1963), Goldfinger (1964), Thunderball (1965), and You Only Live Twice (1967).
He returned to the role twice more in Diamonds Are Forever (1971) and Never Say Never Again (1983).
Bond was Connery’s breakthrough role following a decade of stage and TV roles in the 1950s.
Dana Broccoli, the wife of the film series’ producer Albert Broccoli, is said to have persuaded her husband to select Connery for the role despite initial opposition from Ian Fleming, the character’s creator.
Fleming felt Connery was too unrefined, stating: “He’s not what I envisioned of James Bond looks.”
The author was won over by Connery’s performance in Dr No and, in his 1964 novel You Only Live Twice, wrote Connery’s heritage into the character’s background.
Connery became disillusioned with the role towards the end of his tenure, with his friend, Sir Michael Caine, revealing in an interview: “If you were his friend in these early days you didn’t raise the subject of Bond. He was, and is, a much better actor than just playing James Bond, but he became synonymous with Bond. That was upsetting to him.”
Post-Bond, Connery starred alongside Caine in adventure film The Man Who Would Be King (1975), Time Bandits (1981) and Steven Spielberg’s 1989 sequel Indiana Jones and the Last Crusade.
He played the Harrison Ford character’s father, Henry Jones Sr.
Connery won his only Oscar for the role of Jimmy Malone in Brian De Palma’s 1987 gangster film The Untouchables.
Other famous credits include fantasy film Highlander (1986), action thriller The Rock (1996) and adventure flop The League of Extraordinary Gentlemen (2003), which is widely believed to have prompted his retirement from acting.
Connery – who was knighted by the Queen in 2000 – is said to have detested his experience so much that he had no desire to return the profession.
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