The 'Private Benjamin' star - who played Goldie Hawn's character Judy Benjamin's tough commanding officer Doreen Lewis in the 1980 movie - passed away at her home in Burbank, California, on Sunday after losing her battle with bladder cancer.
Her family said in a statement: "Our family is so grateful for the outpouring of love and respect for Eileen. She was funny and caring and truly one of a kind. Her strength and love will never be forgotten."
Goldie took to Twitter to pay tribute to the late Hollywood icon, insisting the 'Jeepers Creepers' star was the funniest actress she ever worked with.
She wrote: "We have lost my old friend Eileen Brennan. No one ever made me laugh more! Now I cry. Please keep singing darling from on high. Rest (sic)"
Brennan earned a Best Supporting Actress Oscar nomination for her role in 'Private Benjamin' and won an Emmy for reprising the part in the TV version of the movie.
She also received Emmy nominations for her guest roles in TV series including 'Will & Grace' - in which she portrayed Zandra - as well as 'Taxi', 'Newhart' and baby boomers show 'Thirtysomething'.