In a letter, Jobs had recommended Cook, 50, to the board. His eventual appointment had been expected.
The Wall Street Journal says the timing of the announcement, however, was a surprise and raised questions about the health of Jobs, who was diagnosed with a rare form of pancreatic cancer in 2004 and underwent a liver transplant two years ago.
Still, it seems unlikely the board would have named Jobs chairman if his health had entered a new, more serious phase.
In late trading, Apple's stock recently sold for $355.50, down $21, or 5.5%. It closed in regular trading at $376.18, up 2.6%.
Related: Here's The New York Times' story, and USA Today's.
Full text of Jobs' letter
To the Apple Board of Directors and the Apple Community:
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.
I hereby resign as CEO of Apple. I would like to serve, if the Board sees fit, as Chairman of the Board, director and Apple employee.
As far as my successor goes, I strongly recommend that we execute our succession plan and name Tim Cook as CEO 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.