Cook died of respiratory failure on Tuesday, surrounded by friends and family at her home in Manhattan, according to her publicist. She was 89 years old.
Cook rose to fame in the '50s as the lead in such Broadway musicals as Plain and Fancy and Candide, among others. She won a Tony Award for her role in The Music Man, in which she played Marian, a librarian who falls for a con artist.
After a few personal setbacks, including a struggle with alcohol abuse, she revived her career in the '70s, performing in cabarets and concert halls.
Cook received Kennedy Center Honors from Barack Obama in 2011. Broadway greats Audra McDonald, Patti LuPone, Glenn Close and Sutton Foster among others paid tribute to the legend with a medley of her best-known songs.
Just last June, she published her autobiography, Then & Now: A Memoir, in which she got candid about her struggles with depression, alcoholism and obesity.