Brennan's managers, Jessica Moresco and Al Onorato, said she passed away Sunday at home in Burbank after a battle with bladder cancer.
"Our family is so grateful for the outpouring of love and respect for Eileen," her family said in a statement. "She was funny and caring and truly one of a kind. Her strength and love will never be forgotten."
Brennan got her first big role on the New York stage in "Little Mary Sunshine," a musical comedy that won her the 1960 Obie award for best actress. Along with her "excellent singing voice," her performance was "radiant and comic," said a New York Times review.