Jobs, a Palo Alto resident who underwent a liver transplant in 2009, has been on medical leave from Apple since January, saying he wants to focus on his health.
In today's resignation letter, Jobs said he "strongly recommended" that the company "execute our succession plan and name Tim Cook as CEO of Apple."
Cook has led the company during Jobs' most recent medical leave, as well as during absences for the 2009 liver transplant and treatment for pancreatic cancer in 2004.
Jobs said he would like to continue serving as Apple's board chairman and as an Apple employee.
"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," he said in today's letter.
Art Levinson, chairman of Genentech and a member of Apple's board of directors, commented on Jobs' guidance and leadership in a press release.
"Steve's extraordinary vision and leadership saved Apple and guided it to its position as the world's most innovative and valuable technology company," Levinson said. "Steve has made countless contributions to Apple's success, and he has attracted and inspired Apple's immensely creative employees and world class executive team. In his new role as Chairman of the Board, Steve will continue to serve Apple with his unique insights, creativity and inspiration."
The board confirmed Cook's promotion to CEO.