The British character actor was nominated for an Oscar and won a Golden Globe for his performance in the 1968 Charles Dickens adaptation.
He appeared in EastEnders as Edwin Caldecott, an old nemesis of Jim Branning, and played wizard Merlin in Disney's A Kid in King Arthur's Court.
His widow Therese said he would be "greatly missed".
"He brought joy to his family and to the hearts of many and will be greatly missed. He was singing until the end," she said.
Moody was born Ronald Moodnick in Tottenham, north London, on 8 January 1924, the son of Jewish immigrants. His father anglicised the family name to Moody several years later.
He had originally planned to be an economist and did not take up acting seriously until his late 20s.
His big break came in the 1960s when he was given the part of Fagin, the leader of a band of juvenile rogues and pickpockets, in Oliver!, the musical version of Dickens's Oliver Twist.