The 64-year-old actor, who is the fifth star to essay the role of British spy 007, said the late artiste paved the way for other actors to portray Bond on screen, reported People magazine.
"Sir Roger Moore was the greatest Bond of his time. He embraced the role with an easy charm and grace that let us all in on the game.
"He saved the world seven times and then went on to become an even greater man working to 'save the children' with UNICEF," Brosnan said.
"He never forgot the audience and we shall never forget him. I am proud to have followed in your footsteps Sir Roger. My heartfelt condolences to his family, friends and children," he said.
Moore was the only actor who portrayed the popular fictional spy in seven movies between 1973 and 1985.
Brosnan, on the other hand, played 007 in four films from 1995 to 2002 which include, "Tomorrow Never Dies", "The World Is Not Enough" and "Die Another Day".