Holm, a star of the Broadway stage and movies, was admitted to New York's Roosevelt Hospital a week ago, but her husband took her home to her Manhattan home on Friday, Phillips said.
Holm won the best supporting actress Academy Award for "Gentleman's Agreement" in 1947. She was nominated for the same honor in 1949 for "Come to the Stable" and 1950 for "All about Eve," according to the Academy database.
Holm's stage career began in 1936 in a Deer Lake, Pennsylvania, stock company, which led to an understudy role in a touring production of "Hamlet" with Leslie Howard, according to her official biography.
Her Broadway debut in "The Time of Your Life" in 1939 was a small part, but it brought her to the attention of New York critics. Four years later, she was cast as Ado Annie in the smash "Oklahoma!" because of her ability to "sing bad," the biography said.
She signed a long-term contract with 20th Century Fox that began her film career in 1945, after she toured Europe entertaining troops with the USO. Her first Fox movie was "Three Little Girls in Blue" in 1946, a supporting role that earned her star billing for the musical "Carnival in Costa Rica" in 1947.
Holm's stardom took off in her third film, "Gentleman's Agreement," in which she won the best supporting actress Academy Award for playing fashion editor Anne Dettry.
Her official biography said she was challenged in "finding parts appropriate for this intelligent blonde who didn't fit their Betty Grable 'pin-up girl' mold." In 1949, however, she was cast as a "tennis-playing French nun in "Come to the Stable," which earned her another best supporting actress Oscar nomination, it said.
Fox briefly suspended her in 1950 "for refusing other roles she felt were beneath her." But she was brought back that same year to play the role of Karen Richards in "All About Eve." She was again nominated for the best supporting actress Oscar.
She shocked Hollywood by buying out her Fox contract after "All About Eve" to return to Broadway, despite her rising big screen stardom. Once back in New York, Holm also began a long career acting in television.
Her TV resume includes dozens of series, starting as a guest actress with "All Star Revue" in 1950 and concluding with an episode of "Whoopi" in 2004. In between, she had her own short-lived series "Honestly, Celeste!" in 1954. She is also remembered as the Fairy Godmother in Rodgers and Hammerstein's "Cinderella," a 1965 television series.
She played Hattie Greene in both the "Touched by an Angel" and "Promised Land" TV series in the 1990s.
The last decade of her life was overshadowed by a bitter legal dispute between one of her two sons and Holm's fifth husband, Frank Basile. She married Basile, who was 46 years younger than her, in 2004.
Neither of her two sons was there in her Central Park West apartment when she died, Phillips said.
She first married director Ralph Nelson in 1938, but the couple divorced the next year after the birth of a son, Ted, according to her official biography.
Her second marriage, to English auditor Francis Davies, in 1940 also ended quickly, the biography said.
Holm married airline public relations executive A. Schuyler Dunning in 1946. Her second son, Daniel, was born that year, but that marriage did not last, it said.
However, Holm's fourth marriage in 1961 to actor Wesley Addy, whom she met while co-starring in the 1960 Broadway production of "Invitation to the March." They often acted onstage together during their marriage, which lasted until Addy's death in 1996.
Funeral arrangements were not immediately available.