Murray, who also holds non-exec director posts at media and telecoms firm Thomson, Knowledge Peers and Tangent Communications, will chair Royal Mail's audit and risk committee when he takes up the role in August.
He was previously the senior independent director of market research company TNS, where he spent three years. Other posts Murray has held include that of finance director at broadcasting firm Carlton Communications.
Donald Brydon, Royal Mail's group chairman, said: "Paul's extensive experience in business, including his management skills in both consumer and service industries and his experience of regulated, competitive markets, will be an asset to Royal Mail as it continues to drive forward its modernisation."
Murray said: "I am looking forward very much to joining the board team at Royal Mail as it gets on with the challenges of transforming its operations to compete successfully against growing competition, especially from electronic media, while continuing to provide the essential mails and Post Office services relied on every day."