Jobs died "peacefully," surrounded by family members, his family said in a statement.
Neither Jobs' family nor Apple revealed where he died or from what cause, though in recent years Jobs had fought a form of pancreatic cancer and had a liver transplant.
"We are deeply saddened to announce that Steve Jobs passed away today," read a statement by Apple's board of directors. "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."
As Jobs' death was announced, the homepage of Apple's website switched to a full-page image of Jobs with the text, "Steve Jobs 1955-2011."
Clicking on the image revealed additional text that was credited to current Apple CEO Tim Cook in a separate memo to Apple employees.
"Apple has lost a visionary and creative genius, and the world has lost an amazing human being," the text read. "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."
Reaction to Jobs' death came from far and wide -- even from the White House.
"Michelle and I are saddened to learn of the passing of Steve Jobs," President Obama said in a written statement. "Steve was among the greatest of American innovators - brave enough to think differently, bold enough to believe he could change the world, and talented enough to do it."
Shortly after learning of Jobs' death, Wozniak told ABC News, "I'm shocked and disturbed."
Jobs co-founded Apple Computer in 1976 and, with his childhood friend Steve Wozniak, marketed what was considered the world's first personal computer, the Apple II.
Later, on ABC News' "Nightline," he said it was hard to imagine, in some ways, how the world would move forward without Jobs.
"You get shocked when people you know die," Wozniak said. "And this was closer to when John Lennon died, or JFK or Martin Luther King."
Industry watchers called Jobs a master innovator -- perhaps on a par with Thomas Edison -- changing the worlds of computing, recorded music and communications.