Jobs died peacefully, surrounded by family members, his family said in a statement. In recent years Jobs had fought a form of pancreatic cancer and had a liver transplant.
"Steve's brilliance, passion and energy were the source of countless innovations that enrich and improve all of our lives," read a statement by Apple's board of directors. "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."
Jobs co-founded Apple Computer in 1976 and, with his childhood friend Steve Wozniak, marketed what was considered the world's first successful personal computer, the Apple II.
Industry watchers called Jobs a master innovator -- perhaps on a par with Thomas Edison -- changing the worlds of computing, recorded music and communications.
"I'm shocked and disturbed," said Wozniak when reached by ABC News. 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."
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 brought one to additional text that was attributed to Apple's current CEO, Tim Cook.
"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.
"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."
Jobs' rivals in the development of personal computers, Microsoft co-founders Bill Gates and Paul Allen, immediately reacted to his death and highlighted his importance to their industry.
Allen called him "a unique tech pioneer and auteur who knew how to make amazingly great products."
Gates said, "Steve and I first met nearly 30 years ago, and have been colleagues, competitors and friends over the course of more than half our lives.
"The world rarely sees someone who has had the profound impact Steve has had, the effects of which will be felt for many generations to come," Gates said. "For those of us lucky enough to get to work with him, it's been an insanely great honor. I will miss Steve immensely."
Facebook founder Mark Zuckerberg said, "Steve, thank you for being a mentor and a friend. Thanks for showing that what you build can change the world. I will miss you."
Jobs continued to create in recent years despite his failing health. He took three medical leaves from Apple.
In 2004, he beat back an unusual form of pancreatic cancer, and in 2009 he was forced to get a liver transplant. Jobs finally announced on Aug. 24, 2011 that he was stepping down as Apple's chief executive.
"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," Jobs wrote in his letter of resignation. "Unfortunately, that day has come."
He remained as chairman of the corporation, a new position created for him.