In an announcement made this afternoon, the computer company said it was "deeply saddened" to announce that he had died.
"Steve's brilliance, passion and energy were the source of countless innovations that enrich and improve all of our lives. The world is immeasurably better because of Steve.
"His greatest love was for his wife, Laurene, and his family. Our hearts go out to them and to all who were touched by his extraordinary gifts. "
Apple has also posted a tribute on its site:
"Apple has lost a visionary and a creative genius, and the world has lost an amazing human being. 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 always be the foundation of Apple."
He is survived by his wife Laurene, with whom he had three children. He also had a daughter with a woman he dated prior to marrying.
Jobs's death came the day after Apple unveiled the new iPhone 4S at its headquarters in Cupertino, California.
Jobs, 56, underwent an operation for pancreatic cancer in 2004 and a liver transplant in 2009.
He was the mind behind the iPhone, iPad and other devices that turned Apple into one of the world's most powerful companies.
He took indefinite leave from Apple in January and resigned as chief executive in August, saying he could not longer perform the role.
In a letter addressed to Apple's board and the "Apple community,'' Jobs said he "always said if there ever came a day when I could no longer meet my duties and expectations as Apple's CEO, I would be the first to let you know. Unfortunately, that day has come.''
Jobs shepherded Apple from a two-man startup to Silicon Valley darling when the Apple II, the first computer for regular people to really catch on, sent IBM Corp. and others scrambling to get their own PCs to market.
After Apple suffered a slump in the mid-1980s, he was forced out of the company. He was CEO at Next, another computer company, and Pixar, the computer-animation company that produced "Toy Story'' on his watch, during the 10 years before he returned.
- HERALD ONLINE