The postal operator is seeking a marketer with greater commercial marketing experience than Rich as it faces competition from new entrants to the market.
Rich's promotion in June 2002 from director of corporate development to marketing chief surprised industry observers. Many had expected Royal Mail managing director Gillian Wilmot to be given the role.
A Royal Mail spokesman confirmed the company was searching for Rich's replacement. It is not yet known whether the recruit will sit on Royal Mail's board.
Rich will continue to oversee marketing for Royal Mail until his successor is found. The spokesman said that 'another senior role' would be found for him within the organisation.
This week Crozier also announced he had cut Royal Mail's management board from 11 to eight. In addition to Rich, Paul Bateson, managing director of logistics, and Vanessa Leeson, managing director of Parcelforce, have left the board.
Last month Royal Mail announced that it had failed to meet any of the 15 targets for minimal acceptable service set for it by watchdog Postcomm.