She was 65.
Cole's death was confirmed by publicist Maureen O'Connor.
Notables were quick to express their condolences.
"#NatalieCole, sister beloved & of substance and sound. May her soul rest in peace," tweeted the Rev. Jesse Jackson.
"A voice from heaven has been called home," added Cher in a tweet
Born in 1950, Cole grew up among musical royalty. Her father was one of the most accomplished singers and jazz musicians of the postwar era, and her mother, Maria Hawkins Cole, was a singer for Duke Ellington. Their house, in Los Angeles' upscale Hancock Park neighborhood, was a regular spot for her parents' colleagues.
"I remember meeting Peggy Lee, Danny Thomas, Lena Horne, Dorothy Dandridge, Ella Fitzgerald, Louis Armstrong and so many others at parties," she told The Wall Street Journal in 2014
Tony Bennett, who also knew many of the legends of that era, expressed his sadness on Instagram on Friday.
"I am deeply saddened to hear of the passing of Natalie Cole, as I have cherished the long friendship I had with her, her father Nat, and the family over the years," he wrote.
At age 6, Cole sang with her father on a Christmas album, and she was performing by the time she was 11. Nat King Cole died in 1965, when she was 15, a loss that "crushed" her, she said.
"Dad had been everything to me," she told the WSJ.
After college in Massachusetts, Cole embarked on her own career. In 1975, she had a massive hit with "This Will Be" from her album "Inseparable," which showed off her tremendous pipes -- she earned comparisons to Aretha Franklin -- and command of a range of styles. The work won her a Grammy for best new artist.
She followed that with other hits, including "I've Got Love on My Mind," "Our Love" and "Someone That I Used to Love."
But failing sales and personal problems sidetracked Cole's career. She had done heroin in the early '70s, she told the Houston Chronicle
, and then got hooked on cocaine. Her mother even filed for conservatorship in 1982.
A rehab stint in 1983 turned her life around, she said.
"Somehow, at some point halfway through those 30 days, I went from not wanting to be there to being afraid to leave. I was starting to get it," she said.
Cole began a comeback in the late '80s that was capped by 1991's "Unforgettable ... With Love," an album that -- thanks to the wonder of technology -- included a duet with her father on one of his biggest hits, "Unforgettable." (On another song, "Route 66," she was accompanied on piano by another member of her family, her uncle Ike Cole.)
For years, she had declined to perform her father's works in concert; now, an album of those recordings won six Grammys, including the big three: song of the year, record of the year and album of the year.
She won another Grammy for 2008's "Still Unforgettable," which included a variety of American standards.
Longtime Grammy producer Ken Ehrlich remembered Cole as having "one of those magical voices that grabbed you from the first note."
"In a way, and not just in lineage, Natalie was the connector between the great singers of her father and Ella's generation, and the great female voices who were to dominate in the last 25 years," he said in a statement. "I'll never forget when we did 'Unforgettable' as a duet with her father's recording on a Grammy hall of fame show, years before she recorded it. Magical!"
In 2008, Cole started suffering from kidney problems due to hepatitis C, which she attributed to her past drug issues. Despite chemotherapy, both kidneys failed, and in 2009, she went public with a request for a kidney donation.
Even then, despite her struggles, she was a determined performer.
"I have been on dialysis in Istanbul, Milan, Indonesia, Manila, London. It's -- it's amazing," Cole told CNN in 2009
She received a directed donation of a kidney from a deceased donor in May 2009.
Cole maintained her recording and performing career, most recently recording an album in Spanish, "Natalie Cole in Español." She also appeared as a judge on "RuPaul's Drag Race" and guested on some "Real Housewives" programs.
Cole was married three times. She divorced her third husband, Kenneth Dupree, in 2004.