The Irish actor was frequently seen on Broadway after his debut in Philadelphia. His other credits include A Day in the Death of Joe Egg, in which he replaced star Albert Finney, Sleuth, Faith Healer, The Elephant Man, Execution of Justice, Sherlock's Last Case, Ghetto, and Dancing at Lughnasa. His last appearance on Broadway was in Translations in 1995.
In addition to his stage work, Donnelly was frequently seen in films. Among his screen credits are The Knack...and How to Get It, John Huston's adaptation of James Joyce's The Dead, Godfather Part III, and Twister.