Brennan's managers said she died Sunday at home after a battle with bladder cancer.
"She was funny and caring and truly one of a kind. Her strength and love will never be forgotten," Brennan's family said in a statement.
Her long resume included her Oscar-nominated work in "Private Benjamin," where she played gruff Army Capt. Doreen Lewis.
She 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. But it was a series of sharp-tongued roles that won her fans on television and in movies. She was the aloof Mrs. Peacock in 1985's "Clue" and the mean orphanage superintendent Miss Bannister in 1988's "The New Adventures of Pippi Longstocking."
"Our world has lost a rare human," said "Private Benjamin" star Goldie Hawn in a statement. "Eileen was a brilliant comedian, a powerful dramatic actress and had the voice of an angel. I will miss my old friend."
Brennan is survived by her two sons, Sam and Patrick Brennan.
The Associated Press contributed to this report.