He appeared in seven Bond films between 1973 and 1985, including Live and Let Die, The Spy Who Loved Me and For Your Eyes Only.
Sir Roger's family confirmed the news on Twitter, saying he had died after "a short but brave battle with cancer".
The statement from his children Deborah, Geoffrey and Christian, read: "Thank you Pops for being you, and being so very special to so many people."
"With the heaviest of hearts, we must share the awful news that our father, Sir Roger Moore, passed away today. We are all devastated," they said.