The 56-year-old Jobs, who has been suffering health problems since 2004, will remain with the firm as chairman.
"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. Unfortunately, that day has come," the father of the iPod, iPhone and iPad said in his letter of resignation.
"As far as my successor goes, I strongly recommend that we execute our succession plan and name Tim Cook as CEO of Apple," Jobs said.
The Apple founder, who was diagnosed with pancreatic cancer in 2004 and underwent a liver transplant in 2009, did not provide any details on why he decided to resign now.
Cook has been Apple's acting CEO since Jobs went on medical leave in January.
"The Board has complete confidence that Tim is the right person to be our next CEO," co-lead director Art Levinson said in a statement.
"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," Levinson, the chairman of Genentech, said.