He was 56 and had battled pancreatic cancer since 2004.
"Apple has lost a visionary and creative genius, and the world has lost an amazing human being," the company said in a statement. "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."
In a separate statement, his family said, "Steve died peacefully today surrounded by his family. ... In his public life, Steve was known as a visionary; in his private life, he cherished his family. We are thankful to the many people who have shared their wishes and prayers during the last year of Steve's illness."