Originally intending to become a composer, Stuart dropped out of college to follow a career in film, working as an assistant editor to avant-garde filmmaker Mary Ellen Bute, before going on to work as a film researcher for Walter Cronkite's series, The Twentieth Century. In 1959 Stuart met one of his self-described “guardian angels,” film and television producer David L. Wolper. The two went on to form a long and successful creative and business partnership, producing and directing several documentaries including The Making of the President, The Rise and Fall of the Third Reich, Four Days in November, and Wattstax.
Not limiting himself to solely documentaries, Stuart ventured into feature films with If It's Tuesday, This Must Be Belgium (1969) and Willy Wonka & the Chocolate Factory. Stuart continued working well into his seventies, directing and producing the well-received The Hobart Shakespeareans (2005) and The Poet's View (2004). Among the many acknowledgements of his work have been five Primetime Emmy nominations, winning in 1963 for the documentary The Making of the President 1960, a Peabody Award, and an Oscar nomination for Four Days in November.