Jobs says he loves Apple and hopes to be back as soon as he can. He says he and his family would appreciate respect for their privacy.
Cook took the company reins when Jobs, a pancreatic cancer survivor, went on medical leave from January through June 2009.
It was Cook's second stint leading Apple. Cook, who joined Apple in 1998, ran the Cupertino, Calif.-based company for two months in 2004 while Jobs recovered from surgery for pancreatic cancer. His performance then won him the promotion to chief operating officer in 2005.
Analysts credit Cook with solving problems that Apple was having with inventory management. Many people consider Cook as Jobs' logical successor.
Under Cook's direction in 2009, the company kept cranking out well-received products including updated laptops with lower entry-level prices and a faster iPhone with many longed-for features. Apple sold more than a million of the new iPhone 3GS during its first three days on the market.