The 56-year-old stood aside as Apple chief executive on August 24 citing health problems, but remained on the board of directors.
He had earlier battled pancreatic cancer in 2004 and had received a liver transplant in 2009.
“Apple has lost a visionary and creative genius, and the world has lost an amazing human being,” Apple said in a statement posted on their website.
“Those of us who have been fortunate enough to know and work with Steve have lost a dear friend and an inspiring mentor.
“Steve leaves behind a company that only he could have built, and his spirit will forever be the foundation of Apple.”
He is survived by his wife Laurene and four children.