The move appears to be the result of an unspecified medical condition for which he took an indefinite leave from his post in January. Apple's chief operating officer, Tim Cook, has been named CEO.
In a letter addressed to Apple's board and the "Apple community," Jobs said he "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. Unfortunately, that day has come."
Jobs' health has long been a concern for Apple investors who see him as an industry oracle who seems to know what consumers want long before they do. After his announcement, Apple stock quickly fell 5.4 percent in after-hours trading.
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The company said Jobs gave the board his resignation Wednesday and suggested Cook be named the company's new leader. Apple said Jobs was elected board chairman and Cook is becoming a member of its board.
Jobs' hits seemed to grow bigger as the years went on: After the colorful iMac computer and the now-ubiquitous iPod, the iPhone redefined the category of smart phones and the iPad all but created the market for tablet computers.
His own aura seemed part of the attraction. On stage at trade shows and company events in his uniform of jeans, sneakers and black mock-turtlenecks, he'd entrance audiences with new devices, new colors, new software features, building up to a gran finale he'd predictably preface by saying, "One more thing."
After Apple suffered slump in the mid-1980s, he was forced out of the company. He was CEO at Next, another computer company, and Pixar, the computer-animation company that produced "Toy Story" on his watch, during the 10 years before he returned.
The January leave was Jobs' third medical leave over several years. He had previously survived pancreatic cancer and received a liver transplant.