By the early 1930s she had established herself as one of the greatest theatre actresses of her era and she was a major star on Broadway throughout the 1930s, 1940s, and 1950s. In 1931, she played the Unknown Woman in the American premiere of Luigi Pirandello's As You Desire Me, filmed the following year with Greta Garbo in the same role. This was followed by Eugene O'Neill's Mourning Becomes Electra, Luigi Chiarelli's The Mask and the Face, opposite Humphrey Bogart, and Zoe Akins' The Old Maid, in the role later played on film by Bette Davis. In 1936, she played Gertrude to John Gielgud's Hamlet in a production which also featured Lillian Gish as Ophelia.
In 1937, she joined the Old Vic Company in London and played Lady Macbeth opposite Laurence Olivier in a production by Michel Saint-Denis, at the Old Vic and the New Theatre. In 1941, she played Lady Macbeth again in New York opposite Maurice Evans in a production staged by Margaret Webster, a role she was to reprise later on television twice (the second version was released to theatres in Europe as a feature film, and was the first Macbeth in Technicolor).
In 1942-1943, she played Olga in Chekhov's Three Sisters, in a production which also featured Katharine Cornell, Ruth Gordon, Edmund Gwenn, Dennis King, Alexander Knox and Kirk Douglas in his Broadway debut. The production was so illustrious, it made it to the cover of Time .
In 1947, she triumphed as Medea in a version of Euripides' tragedy, written by the Poet Robinson Jeffers and produced by John Gielgud who also played Jason. She won the Tony Award for Best Actress for her performance. She toured in this role to Germany in 1951 and to France and Australia in 1955-56. In 1953, she was directed by Charles Laughton in his own adaptation of Stephen Vincent Benét's John Brown's Body with a cast also featuring Raymond Massey and Tyrone Power. In 1960, she played Madame Arkadina in Chekhov's The Seagull first at the Edinburgh Festival, and then at the Old Vic, with Tom Courtenay, Cyril Luckham and Tony Britton.
In 1970 she realised a long held ambition to play the role of Hamlet. She did this on a national tour of the United States and at New York's Carnegie Hall at the age of 73.
In 1982, she returned to Medea, this time playing the Nurse opposite Zoe Caldwell in the title role. Caldwell had appeared in a small role in the Australian tour of Medea in 1955-1956. Anderson was also nominated for the Tony for Best Supporting Actress.
In Hollywood, her striking and not conventionally attractive features meant that her opportunities were limited to supporting character actress work. She naturally preferred the stage in any event. However, she did make a handful of significant films. In particular, she was nominated for a Best Supporting Actress Oscar for her role in Alfred Hitchcock's Rebecca (1940). As the housekeeper Mrs. Danvers, Judith Anderson was required to mentally torment the young bride, the "second Mrs. de Winter" (Joan Fontaine), even encouraging her to commit suicide; and taunt her husband (Laurence Olivier) with the memory of his first wife, the never-seen "Rebecca" of the title. "Mrs. Danvers" as conceived by Judith Anderson is widely considered one of the screen's most memorable and sexually ambiguous female villains. (The Oscar went to Jane Darwell, for The Grapes of Wrath.)
This led to several film appearances during the 1940s in such films as Lady Scarface (1941), Kings Row (1942), Otto Preminger's Laura (1944) with Gene Tierney, René Clair's And Then There Were None (1945), Ben Hecht's Specter of the Rose (1946), and Jean Renoir's The Diary of a Chambermaid (1946). She continued returning to the New York stage, playing the role of Lady Macbeth twice, and winning a Tony Award in 1948 for her historically acclaimed bravura performance in the title role of Medea.
Her stage and film work continued and by the 1950s she was also appearing in television productions. She played Herodias in Salome (1953), Memnet in Cecil B. de Mille's The Ten Commandments (1956), gave a memorable performance as Big Momma in the film of Tennessee Williams' Cat on a Hot Tin Roof (1958), Evil Stepmother in Cinderfella, and Buffalo Cow Head in A Man Called Horse (1970).
Anderson also recorded many spoken word record albums for Caedmon Audio in the 1950s through the 1970s, including her performance as Lady Macbeth (opposite Anthony Quayle). She received a Grammy nomination for her work on the Wuthering Heights recording.
Anderson was married and divorced twice, first to Benjamin Harrison Lehmann (1937-1939) and second to Luther Greene (1946-1951). Neither marriage, both of which occurred after she turned 40, produced children, but she did serve as godmother for friends' children. Despite her marriages, Anderson was subject to speculation about her sexuality throughout her career. In his biography Otto Preminger: The Man Who Would Be King (2007), Foster Hirsch states matter-of-factly that Anderson was gay, extending this speculation into the current day.
On 10 June 1991, in the Queen's Birthday Honours, she was named a Companion in the Order of Australia (AC), "in recognition of service to the performing arts".