Duke's family released a statement through her publicist.
"This morning, our beloved wife, mother and matriarch and the exquisite artist, humanitarian and champion for mental health, Anna Patty Duke Pearce, closed her eyes, quieted her pain and ascended into a beautiful place. We celebrate the infinite love and compassion she shared through her work and throughout her life."
Born Anna Marie Pearce, some of Duke's earliest acting roles were in daytime soap operas. In the late 1950s, she played Ellen Williams Dennis in CBS' The Brighter Day, and appeared as Molly Scharf in NBC's Kitty Foyle.
She followed on her early success playing the young Helen Keller in 1962's The Miracle Worker with a popular sitcom, The Patty Duke Show, which aired from 1963-1966. She played identical cousins living in Brooklyn Heights, New York.
In 2015, she played twin roles again: as a pair of grandmas on an episode of Liv and Maddie, a series on the Disney Channel.
Duke had a difficult childhood with abusive parents. By eight years old she was largely under the control of husband-and-wife talent managers who soon found her work on soap operas and print advertising. In the meantime, they supplied her with alcohol and prescription drugs, which accelerated the effects of her undiagnosed bipolar disorder.
In her 1988 memoir, "Call Me Anna," Duke wrote of her condition and its diagnosis only six years earlier, and of the treatment that subsequently stabilized her life. The book became a 1990 TV film in which she starred, and she became an activist for mental health causes, helping to de-stigmatize bipolar disorder.
In addition to the Academy Award she took home at age 16, Duke won three Emmys at the height of her career for roles in My Sweet Charlie, Captains and the Kings and the TV adaptation of The Miracle Worker. She also won two Golden Globes, one for Most Promising Newcomer in 1963 and another for her role in Me, Natalie in 1970.
In 2013, she guest-starred on FOX's primetime serial Glee.
The actress is survived by her husband Michael Pearce, her sons from previous relationships Sean Astin and Mackenzie Astin and another son whom she adopted with Pearce.
She was previously married to Harry Falk, Michael Tell and John Astin. She also had a widely publicized relationship with Desi Arnaz Jr.