In a brief statement, Apple's Board of Directors said "we are deeply saddened to announce that Steve Jobs passed away today."
"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."
The Board said Jobs' 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," it said.
In a separate statement, his family said Jobs "died peacefully today surrounded by his family...We know many of you will mourn with us, and we ask that you respect our privacy during our time of grief."
Jobs was a pancreatic cancer survivor and had undergone a liver transplant several in 2009. He had been on a leave of absence since January this year -- his third since his health problems began -- and stepped down as Apple CEO in August, handing over the reins of the company to Tim Cook.
He started Apple with a high school friend in a Silicon Valley garage in 1976. But after a decade, he was forced out of the company but returned in 1997 to save the company which was in dire financial straits. It had lost more than USD 800 million in a year.
After Jobs stepped in as interim chief. He slashed unprofitable projects and narrowed the company's focus. He presided over a new marketing push to set the Mac apart from Windows, starting with a campaign encouraging computer users to "Think different."
During his second stint, it grew into the most valuable technology company in the world.