He passed away at his home in Beverly Hills on Thursday (August 10) following a battle with cancer, BBC News reports.
Stuart started his career working on documentaries, before directing the adaptation of Roald Dahl's Charlie and the Chocolate Factory in 1971.
He worked on other feature films such as If It's Tuesday, This Must Be Belgium and won an Emmy for documentary The Making of the President, 1960.
Stuart was nominated for an Oscar in 1965 for his documentary Four Days in November, about the assassination of John F Kennedy.
He is survived by sons Andrew and Peter and daughter Madeline.
Watch Veruca Salt sing 'I Want It Now' in Willy Wonka & the Chocolate Factory below: