John Rishton, who has been at the company since 2011, said it was “time for a change in lifestyle”.
Warren East was head of UK chipmaker Arm Holdings between 2001 and 2013 and has been a non-executive director at Rolls-Royce since the beginning of last year.
He helped turn Arm into a leading developer of chips to major technology companies such as Apple.
Warren East said he was “delighted” to be appointed as the new chief executive.
“[Rolls-Royce] is well positioned in growth markets, with world-class engineering skills and a proud record of innovation and delivery.
“The markets which Rolls Royce serves and the technology it deploys are fascinating. This is a wonderful opportunity and I am very much looking forward to leading this remarkable company.”
John Rishton said: “We have made good progress transforming Rolls-Royce and have a strong team in place. While there is clearly more to do, the company is better placed to face the future.”
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