The British star, who played 007 in seven films, died in Switzerland after a short battle with cancer, Moore's children said on his social media accounts.
"It is with a heavy heart that we must announce our loving father, Sir Roger Moore, has passed away today in Switzerland after a short but brave battle with cancer," Deborah, Geoffrey and Christian Moore wrote.
"The love with which he was surrounded in his final days was so great it cannot be quantified in words alone," the trio added. "Thank you Pops for being you, and for being so very special to so many people."
Moore shared Deborah, Geoffrey and Christian with his third wife, Italian actress Luisa Mattoli. He is also survived by wife Kristina Tholstrup, whom he married in 2002.
"Our thoughts must now turn to supporting Kristina at this difficult time, and in accordance with our father's wishes there will be a private funeral in Monaco," the actor's children said.
With the heaviest of hearts, we must share the awful news that our father, Sir Roger Moore, passed away today. We are all devastated. pic.twitter.com/6dhiA6dnVg— Sir Roger Moore (@sirrogermoore) May 23, 2017
Moore first played James Bond in Live and Let Die (1973), and last portrayed the character in A View to Kill (1985). He later appeared in The Man Who Wouldn't Die, Spice World and Boat Trip, and was also known for his humanitarian work with UNICEF.