Levinson is chairman of Genentech Inc., a pharmaceuticals company he joined as a research scientist in 1980 and led as chief executive from 1995 to 2009. Levinson has been co-lead director on Apple Inc.'s board since 2005. He joined the board in 2000.
Robert Iger, president and CEO of The Walt Disney Co., was tapped as a director.
After taking the reins at Disney in 2005, Iger repaired frayed relations between Jobs and Disney, first by making ABC shows available on iTunes, and then by leading Disney's acquisition of computer animated movie studio Pixar for $7.4 billion. The Pixar deal made Jobs Disney's largest shareholder.
The appointments were announced Tuesday.
Tim Cook, Apple's chief executive, said Levinson has made "enormous contributions" to the company since joining the board, saying "his insight and leadership are incredibly valuable."
Cook said that Iger, 60, was "a great fit for Apple" because his stewardship of Disney is based on principles that Apple shares - generating creative content, using new technology, and expanding into new markets around the world.