Fitzgerald was born William Joseph Shields in Walworth Road, Portobello, Dublin, Ireland, the son of Fanny Sophia (née Ungerland) and Adolphus Shields. His father was Irish and his mother was German. He was the older brother of Irish actor Arthur Shields. He went to Skerry's College, Dublin, before going on to work in the civil service, while also working at the Abbey Theatre. His career with the Abbey Theatre was from 1914–1936 where he was involved in numerous productions.
Fitzgerald went to Hollywood to star in another O'Casey work, The Plough and the Stars (1936), directed by John Ford. He had a successful Hollywood career in such films as The Long Voyage Home (1940), How Green Was My Valley (1941), And Then There Were None (1945), The Naked City (1948) and The Quiet Man (1952).
In 1945, Fitzgerald achieved a unique Academy Awards feat. For portraying Father Fitzgibbon in Leo McCarey's Going My Way (1944), he was nominated for both the Academy Award for Best Supporting Actor (which he ultimately won) and the Academy Award for Best Actor; voting rules were changed shortly after this occurrence to prevent further dual nominations for the same role. An avid golfer, he later accidentally decapitated his Oscar while practicing his golf swing. During World War II, Oscar statuettes were made of plaster instead of gold-plated bronze to accommodate wartime metal shortages. The Academy provided Fitzgerald with a replacement statuette.