The original big screen 007 said he will “miss” Sir Roger, with whom he enjoyed a long friendship “filled with jokes and laughter”.
The longest reigning James Bond died in Switzerland on Monday after a “short but brave battle with cancer”, his family said.
Sir Sean joined Daniel Craig and Pierce Brosnan in mourning their fellow 007 star.
The Scottish actor, 86, said in a statement: “I was very sad to hear of Roger’s passing, we had an unusually long relationship by Hollywood standards, that was filled with jokes and laughter.
“I will miss him.”
In a reference to the theme of Sir Roger’s The Spy Who Loved Me, Craig wrote: “Nobody Does It Better - love Daniel.”
Brosnan, who like Craig has starred as Bond four times, described Sir Roger as “magnificent” as he shared a photograph on Instagram of the pair together.
He wrote: “It is indeed with a heavy heart that I hear the news of your passing this morning.
• READ MORE - Roger Moore remembered: 5 of his most memorable quotes
“You were a magnificent James Bond and one that lead the way for me, the world will miss you and your unique sense of humour for years to come.”
Sir Michael Caine, who enjoyed a close friendship with Sir Roger, posted on Twitter: “I am devastated today at loosing (sic) one of my oldest and closest friends ROGER MOORE, my world will never be the same again.”
The actor’s three children Deborah, Geoffrey and Christian confirmed the actor’s death.
In a statement, they said: “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.”
They said they would focus their attentions on supporting his wife, Kristina, and added that there will be a private funeral held in Monaco in “accordance with our father’s wishes”.
The debonair star added a light-hearted touch to the 007 role during his seven performances.
He wi ll also be remembered for the 1960s TV series The Saint and for his early 1970s show The Persuaders! in which he starred alongside Tony Curtis.
Bond producers Barbara Broccoli and Michael G Wilson said Sir Roger’s “legacy shall live on through his films and the millions of lives he touched”.
Jane Seymour, who starred with Sir Roger in 1973’s Live And Let Die, remembered him as being “funny, kind and thoughtful to everyone around him”.
Among Sir Roger’s Bond films were Moonraker, A View To A Kill and The Man With The Golden Gun.
Off-screen, he was respected for his charity work.
He was made a Commander of the Order of the British Empire (CBE) in 1999 and a Knight Commander of the Order of the British Empire (KBE) in 2003.