On behalf of the Apple's board, Art Levinson, chairman of Genentech, said Jobs's extraordinary vision and leadership saved Apple and guided it to its position as the world's most innovative and valuable technology company.
"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," he said.
"In his new role as chairman of the board, Steve will continue to serve Apple with his unique insights, creativity and inspiration."
Levinson said Cook's 13 years of service to Apple, including filling in for Jobs as acting CEO during his medical leave, meant he was the right person to be Apple's next CEO.
The announcement of Cook as Jobs's replacement was also likely to be welcomed by the industry and the market.
"Investors are very comfortable with Tim Cook even though Jobs has been a driver of innovation ... Tim has shown Apple can still outperform extremely well when he's been acting as CEO," Cross Research analyst Shannon Cross said.
"I don't know if it's a health issue. I don't know if it is a shock. Most likely it was going to happen at some point. Why today versus another day? I don't know."
Jobs' often-gaunt appearance has sparked questions about his health and his ability to continue at Apple.
"I will say to investors: don't panic and remain calm, it's the right thing to do. Steve will be chairman and Cook is CEO," said BGC Financial analyst Colin Gillis.
Bringing Apple back from the dead