Mr Jobs, who underwent a liver transplant following pancreatic cancer, said he could no longer meet his chief executive's duties and expectations.
The Silicon Valley legend will become chairman of the firm.
The 56-year-old has been on medical leave for an undisclosed condition since 17 January.
In a short letter to the board of Apple, Mr Jobs wrote: "I have always said if there ever came a day when I could no longer meet my duties and expectations as Apple's chief executive, I would be the first to let you know.
"Unfortunately, that day has come. I hereby resign as chief executive of Apple.
"I believe Apple's brightest and most innovative days are ahead of it. And I look forward to watching and contributing to its success in a new role.
"I have made some of the best friends of my life at Apple, and I thank you all for the many years of being able to work alongside you."
Apple board member Art Levinson paid tribute to Mr Job's contribution to the company: "Steve's extraordinary vision and leadership saved Apple and guided it to its position as the world's most innovative and valuable technology company."'Hugely successful' Continue reading the main story
This is a sad day for Apple and for the whole technology industry, as its most charismatic and successful leader of recent years brings down the curtain on an extraordinary career.
Steve Jobs addressed his brief letter of resignation not just to his company's board but to the Apple community - and millions worldwide will feel he was talking to them.
Forceful bosses whose personalities shape everything about their businesses are going out of fashion these days, for good reason many would say.
But Steve Jobs is a rare example of a chief executive who is synonymous with his company, a perfectionist who obsesses over every detail and has been the public face of just about every major product launch in the past decade.
It's difficult to imagine Apple without him - but he's leaving having revived what was an ailing business when he returned in the late 1990s, and turned it into the world's wealthiest company and one which has done more than any other in recent years to shape consumer technology.Analysts said the move was not unexpected, and would have little impact on the day-to-day running of the company.
"Steve is [still] going to be able to provide the input he would do as a chief executive," said Colin Gillis at BGC Financial.
"But Tim has been de facto chief executive for some time and the company has been hugely successful. The vision and the roadmap is intact."
Nor will customers see any real difference, analysts said.
"At the end of the day, consumers don't buy products from Apple because they're from Steve Jobs, they buy them because they meet their needs and they're good products, and they'll continue to do that," Michael Gartenberg from Gartner told the BBC.
However, Apple shares slid more than 5% in after-hours trading, suggesting that some investors were less confident of the company's prospects without Mr Jobs at the helm.
At the same time, shares in two of Apple's main Asian rivals gained. Taiwan-based phone maker HTC rose 4.1%, while South Korea's Samsung Electronics gained 3.2%.
The firms compete with Apple in the smartphone and tablet-PC sector, and have been involved in legal battles with Apple over patent rights. Analysts said that Mr Jobs' departure may make life easier for rivals.
"Maybe this will make the playing field a bit more level," Bryan Ma of IDC Asia-Pacific told the BBC's Asia Business Report.Revolutionary products
Mr Jobs is widely seen as the creative force that has driven Apple to become one of the world's biggest companies.
Thanks to innovative and hugely popular products such as the iPod, the iPhone and more recently the iPad, Apple has become one of the most sought after brands in the world.Continue reading the main story
In the near term, at least the next two three years, Apple will continue to have a fantastic run because it's got its entire roadmap in place which will continue to work seamlessly”End Quote Manoj Menon Frost & Sullivan In the three months to the end of June, the company made a profit of $7.3bn on revenues of $28.6bn. It sold more than 20 million iPhones in the period and 9.25 million iPads.
The company recently became the valuable US firm after its market capitalisation overtook that of oil company Exxon Mobil.
Mr Jobs started Apple in the 1970s and its Macintosh computers became hugely popular in the 1980s.
In 1985, Mr Jobs left the company after falling out with colleagues, only to return in 1997 and begin Apple's transformation by launching the colourful iMac computer.
The iPod, which revolutionised the personal music-player market and spawned myriad copycat devices, was launched in 2002 and lay the foundations for the company's success over the past decade.
Next came the iPhone, which similarly revolutionised the smartphone market, while the iPad confounded some initial scepticism to prove hugely popular.
Many versions of these products have been launched while Mr Jobs has been on medical leave, and new versions that have been planned for months will not be affected by his departure, analysts said.
"In the near term, at least the next two three years, Apple will continue to have a fantastic run because it's got its entire roadmap in place which will continue to work seamlessly," Manoj Menon at Frost and Sullivan told the BBC.