The statement read: "[Cole] responded well to pulmonary arterial hypertension-specific agents over many years, during which she performed many concerts world-wide, but eventually succumbed to intractable right heart failure, an outcome that unfortunately commonly occurs in this progressive disorder."
Natalie had to have the kidney transplant after battling hepatitis and drug problems earlier in her life.
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Her death was announced in a statement from her siblings and son Robert Yancy.
They said: "It is with heavy hearts that we bring to you all the news of our Mother and sister's passing. Natalie fought a fierce, courageous battle, dying how she lived ... with dignity, strength and honour. Our beloved Mother and sister will be greatly missed and remain UNFORGETTABLE in our hearts forever. (sic)"
-Bang! Showbiz