Jason Connery, also an actor, told BBC that his father died peacefully in his sleep, while in the Bahamas with many of his family beside him in Nassau.
He added: “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.
“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.”
The Scottish actor was best known for his portrayal of James Bond, being the first to bring the role to the big screen and appearing in seven of the spy thrillers.
His acting career spanned five decades and he won an Oscar in 1988 for his role in The Untouchables. Sir Sean’s other films included The Hunt for Red October, Highlander, Indiana Jones and the Last Crusade and The Rock.
Sean’s death is coming few weeks after the death of popular Hollywood actor, Clark Middleton, who died at the age of 63 after contracting West Nile Virus.