Jobs, a college dropout turned billionaire, was repeatedly quoted as saying, "I want to put a dent in the universe."
Apple paid tribute to its founder in a statement on its website.
"Apple has lost a visionary and creative genius and the world has lost an amazing human being," the statement 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."
Jobs was diagnosed with pancreatic cancer in 2004, and took two subsequent leaves of absence from the company. He received a liver transplant in 2009.
In his resignation letter, Jobs said he had accepted that it was time for him to leave the day-to-day operations.
"I have 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," he said. "Unfortunately, that day has come."
Speculation about his health began immediately upon Apple's announcement that Jobs had resigned as CEO on Aug. 24. He was replaced by longtime Apple executive Tim Cook.
Survivors include his wife, Laurene Powell Jobs, daughters Erin and Eve, and his son, Reed.
Jobs' passing was almost immediately noted on Twitter.
"I'm working on a Mac at work. I have a MacBook and an iPad at home," tweeted Charles Gooch (TheFull90). "I'll be wearing a black mourning turtleneck tonight."
End of an era
Jobs' resignation drew to a close a 35-year career that marked him as a visionary and creative genius.
His place in history began when he and friends Ronald Wayne and Steve Wozniak started Apple Computers in the Jobs' family garage.
Over the years, through a series of product redesigns, strained relationships, and ground-breaking products, Jobs helped build the Apple brand into a mammoth technology company.
During his watch, new life was breathed into the personal computer, the digital music craze was ignited and the way animated pictures were made was turned on its head.
Just four years after the company's founding, its first successful computer, the Apple II – a behemoth personal computer with less memory than your key fob – launched the company onto the market with a value of $1.2 billion on the first day of trading.
But after a series of failed products, company president John Scully began phasing Jobs out. Jobs resigned as Apple CEO in 1985.
"What had been the focus of my entire adult life was gone, and it was devastating," Jobs said during Stanford's 2005 commencement address.
Jobs didn't rest for long. Over the next five years, he started a hardware and software company called NeXT and Pixar, the animation studio that would produce such hits as the "Toy Story" franchise and "Finding Nemo."
Rebirth of a company
Jobs found his way back to Apple in 1997 after Apple bought NeXT and gave him a seat on the board.
By the late '90s, Apple was no longer the company he had left in 1985. By most accounts it was on its deathbed due to poor marketing and pricing.
Jobs took the reins from then-CEO Gil Amelio, becoming its acting CEO and researching ways to reinvigorate his old company.
Next came the "Think Different" campaign, telling potential Apple customers that it was cool to be the misfit, the crazy one who stands apart from the status quo, and use Apple products.
Over the years, Jobs introduced the iMac, iPod, iPhone and iPad, the latter of which looks to have pushed one if its main competitors - Hewlett-Packard - out of the personal computer market completely.
Jobs kept his illness quiet as he searched for alternative cures and treatments, often chalking up his gaunt appearance to unusual diets and nutrition problems.
He made a surprise appearance at the launch of the iPad 2 in March, appearing frail and thin. He was not present at Tuesday's gathering in Cupertino, CA, when an upgrade to the iPhone was announced.
"Steve Jobs will be the Leonardo da Vinci of our time. I cannot think of anyone who comes closer to that description in the last 100 years," David Cohn (Digidave) tweeted.
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