Anderson was only 17 years old when she made her stage debut in 1915 in Sydney and 20 when she first appeared in New York City. After her first major success in New York in 1924 in Cobra, she went on to appear as Nina Leeds in Eugene O'Neill's Strange Interlude (1928) and as Lavinia in O'Neill's Mourning Becomes Electra (1932), among other productions. Her interpretation of Gertrude opposite John Gielgud as Hamlet (1936), of Lady Macbeth in the London (1937) and New York (1941) productions of Macbeth, and in the title role of Robinson Jeffers' version of Medea (1947) are considered the pinnacles of her stage career. Anderson specialized in character portrayals and was at her best in roles of great dramatic intensity.

Anderson also appeared in almost 30 motion pictures, typically playing an evil or sinister matriarchal figure. Among her best-known roles are Mrs. Danvers in Rebecca (1940) and Ann Treadwell in Laura (1944). Her other films include King's Row (1941), Edge of Darkness (1943), and The Strange Love of Martha Ivers (1946). In 1960 she was made Dame Commander of the British Empire.