East was CEO of ARM Holdings from 2001 to 2013. Under his leadership ARM became one of the world's leading developers of semi-conductors. He has been a non-executive director of Rolls-Royce since January 2014.
Ian Davis, chairman of Rolls-Royce, said: "[East] is an engineer by training; he has a deep understanding of technology and of developing long-term partnerships. He has proven strategic and leadership skills in a global business and a strong record of value creation.
"I and all my Board colleagues would like to thank John Rishton for his commitment and leadership. We respect his decision to retire after more than four years of dedicated service. He has led the company during a period of significant growth and transformation. During his tenure profits have increased by 69%, the order book has grown by 24% and the share price has risen 63%."
East said: "I have a strong desire to return to an executive position with the energy and enthusiasm a role like this demands. 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."
As well as being a Non-Executive Director of Rolls-Royce, Warren East serves as a Non-Executive Director on the Boards of BT, De La Rue, Dyson, Micron Inc. and Digital Catapult. His intention is to stand down from all but one of his current roles as a Non-Executive Director, in line with Rolls-Royce company policy.