"We are deeply saddened to announce that Steve Jobs passed away today," the California-based gadgetmaker said in a statement from its 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."
Tim Cook -- who had been handling Apple's day-to-day operations since Jobs went on medical leave in January, and was made CEO in August -- led the praise for the Silicon Valley legend.
"Apple has lost a visionary and 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," he said.
"Steve leaves behind a company that only he could have built, and his spirit will forever be the foundation of Apple."
Apple turned its home page into a tribute to Jobs, posting a large black-and-white photo of the bearded high-tech maestro in his trademark black turtleneck and small round glasses. The only caption: "Steve Jobs, 1955-2011."
When a user clicks on the photo, they are taken to Cook's message in remembrance of Jobs, who died after a long battle with pancreatic cancer.
Apple fans were invited to share their thoughts, memories and condolences by sending messages to email@example.com. The rest of the website and store remained accessible.
Jobs' family also issued a statement, saying he had died surrounded by his relatives.
"In his public life, Steve was known as a visionary; in his private life, he cherished his family," it said.
"We are thankful to the many people who have shared their wishes and prayers during the last year of Steve's illness; a website will be provided for those who wish to offer tributes and memories."
Born on February 24, 1955 in San Francisco to a single mother and adopted by a couple in nearby Mountain View at barely a week old, Jobs grew up among the orchards that would one day become the technology hub known as Silicon Valley.
He was just 21 and Steve Wozniak 26 when they founded Apple Computer in the garage of Jobs's family home in 1976.
Under Jobs, the company introduced its first Apple computers and then the Macintosh, which became wildly popular in the 1980s.
Jobs was elevated to idol status by ranks of Macintosh computer devotees, many of whom saw themselves as a sort of rebel alliance opposing the powerful empire Microsoft built with its ubiquitous Windows operating systems.
Jobs left Apple in 1985 after an internal power struggle and started NeXT Computer company specializing in sophisticated workstations for businesses.
He co-founded Academy-Award-winning Pixar in 1986 from a former Lucasfilm computer graphics unit that he bought from movie industry titan George Lucas.
Apple's luster faded after Jobs left the company, but they reconciled in 1996 with Apple buying NeXT for $429 million and Jobs ascending once again to the Apple throne.
Apple went from strength to strength as Jobs revamped the Macintosh line, revolutionizing modern culture and launching a "post-PC era" in which personal computers give way to smart mobile gadgets -- the iPod, iPhone and the iPad.
His passing will raise doubts over whether the Cupertino, California-based company can continue its dominance in the hugely competitive technology sector.
Jobs 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. (AFP)