Apple chief executive Steve Jobs, who almost single-handedly changed the way people around the world consume music, the Internet and even TV, announced late Wednesday that he has resigned as leader of the company he co-founded in his parents’ garage.

Jobs, who has suffered from pancreatic cancer and had a liver transplant in 2009, has looked increasingly frail in his cultlike appearances in front of Apple fans to introduce new products, but he did not explicitly indicate in a letter to the company’s board and its customers whether his health was failing.

“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,” wrote Jobs, who has been on a health leave of absence since January. “Unfortunately, that day has come.”

Although not entirely unexpected given the grave nature of his previous illnesses — he had surgery for a rare form of pancreatic cancer in 2004 — Jobs’s resignation ends one of the most extraordinary runs in business history. This month, Apple briefly became the most valuable company in the world, surpassing oil giant Exxon Mobil.

Jobs has been replaced by Tim Cook, his longtime No. 2 and the company’s chief operating officer. Cook has run Apple’s day-to-day operations during Jobs’s health-related absences. Jobs will be chairman of the board.

A volatile visionary, a detail-obsessed taskmaster, a lover of simple, understated design in hardware and in software, Jobs over the past three decades has had an outsize, iconoclastic influence on personal computing — first with the Apple II and then the Macintosh computers, then iPods, and now with post-PC devices such as the iPhone and iPad. No other electronics company in the world introduces products that spur massive lines of fans that snake around malls, sometimes for days.

“He’s had a massive impact on personal computing — more important than Bill Gates or anybody else, I think,” said Leander Kahney, editor of the blog Cult of Mac and a longtime computer industry observer. “He has made this company in his image. It functions almost as an extension of his unique personality. There’s really nothing else like it.”

In recent years, as Apple stores have popped up in malls around the country and in iconic locations on several continents — it has a mammoth store in London’s Covent Garden — the company’s reach has stretched beyond its fanboy customers, who disliked Microsoft’s more geeky offerings, and into the lives of everyday consumers. They use the company’s products in their offices, their cars, on their couches and in bed.

Even the stodgy federal government has recently embraced Apple products, deploying iPads, iPhones and Mac laptops to bureaucrats, criminal investigators and doctors. Company executives have said that interest in the iPad by government agencies, schools and colleges has taken them by surprise. Several other companies have tried to match Apple’s recent success with the iPad, but most competing products have not caught on.

Bill Gross, the founder of more than 100 technology companies, wrote on Twitter: “Business superhero Steve Jobs has changed people’s lives around the world more than almost any businessperson alive.”

Jobs is capping his second stint at Apple. He left in 1985 after a brutal battle for control with other executives. He founded another computer company and bought the film company Pixar from George Lucas. Facing near collapse in 1997, Apple brought Jobs back.

Apple’s succession plan has been one of the most closely held secrets in corporate America, but observers said it was not surprising that the company turned to Cook, who is widely credited with running Apple’s intricate teams of designers, engineers and programmers.

“The board has complete confidence that Tim is the right person to be our next CEO,” said Apple board member Art Levinson. “Tim’s 13 years of service to Apple have been marked by outstanding performance, and he has demonstrated remarkable talent and sound judgment in everything he does.”

Still, the prospect of Apple without its visionary-in-chief will spook Apple investors and customers. The company’s stock dropped about 5 percent in after-hours trading Wednesday.

His departure comes at a crucial moment in the battle for the future of computing as companies such as Facebook, Google and Netflix tussle over the flow of information and entertainment. Jobs apparently feels so strongly about the importance of the moment that he emerged from his leave this summer to introduce iCloud, Apple’s way of letting people store their digital lives in the cloud. After the event, he was photographed in a tender embrace with his wife.

Kahney, the Cult of Mac editor, said Apple will probably be in good shape in the short- and medium term. The company is known for mapping out products several years in advance, and Jobs has certainly played a role in those plans.

“While this marks the end of an era for Apple, I think it’s important to remember that there’s more to Apple than any one person, even Steve Jobs,” said Michael Gartenberg, an analyst at Gartner.

Apple and Jobs are “inextricably linked,” said Steven Levy, a senior writer at Wired magazine who has written two books about Apple and chronicled Jobs for more than two decades. But he added that it doesn’t mean the company can’t push on without its founder.

“Every CEO leaves at some point. There’s no such thing as a CEO that goes on forever. People get sick, or they leave,” Levy said, but Jobs has “done a pretty good job” of making sure that the company “doesn’t miss a step.”

Staff writer Brady Dennis contributed to this report.