The fledgling agency picked up the brief following a pitch against undisclosed agencies. Bartle Bogle Hegarty, the incumbent, did not repitch.
Adam & Eve's initial work will focus on the company's flagship Digestives line as it attempts to take market share away from its main rival, United Biscuits' McVitie's range.
Other Cadbury Biscuits brands, which are produced under licence by Burton's Foods, include Fingers and Animals.
Jaspal Chada, the marketing director at Burton's Foods, said: "Adam & Eve is an exciting young company, led by senior industry executives. We are delighted to be working with it and look forward to a productive partnership together."
BBH picked up the Cadbury Biscuits business in September 2005 on the strength of an earlier project for the company.