Her son's resemblance to Orson Welles, with whom she had worked and been linked romantically in the late 1930s, led to rumors Welles was the boy's biological father. Fitzgerald never confirmed this to her son, but in his 2011 autobiography Lindsay-Hogg reported that his questions were resolved by his mother's close friend Gloria Vanderbilt, who wrote that Fitzgerald had told her that Welles was his father.

She studied painting at the Dublin School of Art. Inspired by her aunt, Actress Shelagh Richards, Fitzgerald began her acting career in 1932 at Dublin's famed Gate Theatre. Her great-niece is Actress Tara Fitzgerald. After two seasons there she moved to London, where she found success in British films including The Mill on the Floss, The Turn of the Tide and Cafe Mascot.

Fitzgerald was married to Sir Edward Lindsay-Hogg, 4th Bt., in London on November 18, 1936. She was granted a divorce in Reno on August 30, 1946, after three years of separation. She had one child, Director Michael Lindsay-Hogg during her first marriage, and a daughter, Susan Scheftel, by her second marriage, in 1946, to American businessman Stuart Scheftel.

Fitzgerald's success led her to New York and the Broadway stage in 1938. She made her American debut opposite Orson Welles in the Mercury Theatre production of Heartbreak House. She was seen by Hollywood Producer Hal B. Wallis, who signed her to a contract with Warner Bros. She achieved two significant successes in 1939 — an important role in the Bette Davis film Dark Victory, and an Academy Award nomination for her supporting performance as Isabella Linton in Director william Wyler's Wuthering Heights.

She appeared in Shining Victory (1941), The Gay Sisters (1942) and Watch on the Rhine (1943) for Warner Bros., and Wilson (1944) for Fox, but her career was hampered by her frequent clashes with the management of the studio, and the suspensions that resulted. She lost the role of Brigid O'Shaughnessy, the villainess of The Maltese Falcon (1941), due to her clashes with Jack L. Warner. Although she continued to work frequently throughout the 1940s, co-starring with John Garfield in the Warner Bros. crime drama Nobody Lives Forever (1946), the quality of her roles began to diminish and her career began to lose momentum.

The 1950s provided her with very few opportunities in film, but in the 1960s she asserted herself as a character Actress, and her career enjoyed a revival. Among her successful films of this period were Ten North Frederick (1958), The Pawnbroker (1964) and Rachel, Rachel (1968). Her later films included The Mango Tree (1977) (for which she received an Australian Film Institute Best Actress nomination), and Harry and Tonto (1974), in one scene opposite Art Carney. In the comedy Arthur (1981), she portrayed Dudley Moore's wealthy and eccentric grandmother, even though she was only 22 years older than Moore. Fitzgerald would appear in a Rodney Dangerfield comedy, Easy Money, the horror film Poltergeist II: The Other Side (1986), and the comedy sequel Arthur 2: On the Rocks (1988). Fitzgerald began to act more often on stage and won acclaim for her performance in the 1971 revival of Long Day's Journey Into Night. She achieved success as a theatre director; in 1982 she became one of the first women to receive a Tony Award nomination for Best Direction of a Play, for the production Mass Appeal.

Fitzgerald became a U.S. citizen during World War II in a display of solidarity with her adopted country. In 1946, shortly after completing work on Three Strangers, she left Hollywood to return to New York City where she married her second husband Stuart Scheftel, a grandson of Isidor Straus. She returned to Britain to film So Evil My Love (1948), receiving strong reviews for her performance as an alcoholic adultress, and The Late Edwina Black (1951) before returning to America. She became a naturalised United States citizen on April 18, 1955.

On February 8, 1960, Fitzgerald was recognized with a star, at 6353 Hollywood Boulevard, on the Hollywood Walk of Fame for her contributions to motion pictures.

She appeared frequently on television as well, in such series as Alfred Hitchcock Presents, Robert Montgomery Presents, Naked City, St. Elsewhere, The Golden Girls, and Cagney and Lacey. She was a regular in the short-lived 1965 CBS serial Our Private World. In 1983, she portrayed Rose Kennedy in the mini-series Kennedy with Martin Sheen, and co-starred as Joanne Woodward's mother in the 1985 Alzheimer's drama Do You Remember Love. In 1986, she starred alongside Tuesday Weld and River Phoenix in Circle of Violence about domestic elder abuse. In 1987, she played one of the title roles in the TV sitcom pilot Mabel and Max, produced by Barbra Streisand. She received an Emmy Award nomination for a guest role playing Anna in The Golden Girls Mother's Day episode in 1988 (Fitzgerald played another character in the episode Not Another Monday). She won a Daytime Emmy Award as Best Actress for her appearance in the episode "Rodeo Red and the Runaways" on NBC Special Treat. In 1976 she began a career as a cabaret singer with the show Streetsongs which played three successful runs on Broadway and was the subject of a PBS television special. She recorded an album of the show for Ben Bagley's Painted Smiles label.

A 2015 Welles biography by Patrick McGilligan, however, reports the impossibility of Welles's paternity: Fitzgerald left the U.S. for Ireland in May 1939 and her son (born May 1940) was conceived before her return in late October, while Welles did not travel overseas during that period.