Singer Natalie Cole, the daughter of jazz legend Nat "King" Cole who overcame substance abuse to find stardom in her own right, has died, her family said Friday. She was 65.

The Grammy-winning singer, who had longstanding health issues including complications from a kidney transplant, died on New Year's Eve at a Los Angeles hospital.

"Natalie fought a fierce, courageous battle, dying how she lived - with dignity, strength and honor," her family said in a statement.

Quoting her most identifiable song, the family said: "Our beloved mother and sister will be greatly missed and remain unforgettable in our hearts forever."

In contrast to the rags-to-riches stories of many other artists of her generation, Cole was raised in relative affluence in Los Angeles.

Her career was inextricably linked to that of her father.

She had her first break singing in clubs as the daughter of Nat "King" Cole, but struggled to find her niche as she chose a sound far more modern than her father's standards.

After delving into R&B, soul and pop, Cole achieved her greatest success in 1991 by returning to some of the classics sung by her father.

Her album, Unforgettable... With Love, won the Grammy for Album of the Year.

In a technical feat considered novel in the day, Cole sang the title track - with its elegant, string-backed opening line "Unforgettable, that's what you are" - in a duet with her father, who had died of cancer in 1965.

Cole first made a name for herself in 1975 with the debut song This Will Be (An Everlasting Love) and the album and song Inseparable.

The hits helped Cole win the prestigious Grammy for Best New Artist, one of a total of nine Grammys she earned throughout her career.

"We've lost a wonderful, highly cherished artist and our heartfelt condolences go out to Natalie's family, friends, her many collaborators, as well as to all who have been entertained by her exceptional talent," said a statement from the Recording Academy, which administers the Grammys.

Cole late in her life pursued a career in acting, appearing in several prime-time US series. But her life was marred by personal woes including drug use and three divorces.

In a 2000 autobiography, Angel on My Shoulder, Cole related how she struggled with depression, most painfully after the death of her father and the near-drowning of her son in a swimming pool.

Cole became addicted to crack cocaine and heroin, even at times sharing needles with audience members. She repeatedly sought rehab but later was diagnosed with hepatitis C and liver disease.

She underwent a kidney transplant in 2009, which inspired her second book.

Tony Bennett, the 89-year-old jazz and big band singer who performed both with her and her father, hailed Natalie Cole as "a lovely and generous person who will be greatly missed".

"Natalie was an exceptional jazz singer and it was an honor to have recorded and performed with her on several occasions," Bennett wrote on Instagram.

Cole's final album, released in 2008, was titled Still Unforgettable and expanded on the theme of her 1991 work by adapting classic American tunes in addition to those of her father.

In an interview with People magazine, she said she still wished her father could see her.

"That's the hardest part of this. I think of him every time I sing," she said.