The British star was best known for his Oscar-nominated role as Fagin in Oliver!.
Moody also played Jim Branning's nemesis Edwin Caldecott in EastEnders, and the wizard Merlin in Disney's A Kid in King Arthur's Court.
"He brought joy to his family and to the hearts of many and will be greatly missed. He was singing until the end," his widow Therese said.
Born Ronald Moodnick in Tottenham in 1924, his Jewish father anglicised the family name to Moody several years later.
After originally planning to be an economist, Moody didn't take up acting until he was in his late 20s.
He won a Golden Globe award for playing pickpocket master Fagin in the musical version of Oliver Twist in 1968.
Moody had also said that his biggest regret was turning down the chance to play The Doctor in Doctor Who.