Harper's family confirmed her death to KABC-TV and The New York Times. They didn't reveal the cause, but the actor was diagnosed with terminal brain cancer in 2013. Doctors gave her three months to live at the time.
Last month her husband, Tony Cacciotti said doctors recommended he put her in hospice care, but he declined because he wanted her to remain at home.
Harper is perhaps best known for her role as Rhoda Morgenstern, Mary Richards' best friend and neighbor in The Mary Tyler Moore Show, which ran 1970-77. She got her own show with the spinoff Rhoda, which ran 1974-78. The roles earned her four Emmys and a Golden Globe.
She also earned Golden Globe nominations for her roles in Freebie and the Bean and Chapter Two. She received a Tony nod in 2010 for her role in Looped.
In 2013, she was a contestant on Dancing with the Stars, in which she was eliminated third.
Harper's death comes a week after her 80th birthday.