Godley is responsible for two of the agency's largest clients, Suzuki and Yorkshire Building Society Group.
He will also assume responsibility for the agency's people and processes. Godley will join the agency's board and report to David Miller, the chief executive of The Red Brick Road.
Godley joined The Red Brick Road almost five years ago from DDB London, where he was a business director. Previously he had worked at Saatchi & Saatchi and OgilvyOne.
Miller said: "Andrew has been instrumental in shaping our agency, and contributing to its recent successes. As managing director he'll continue to push our culture and creativity to brave new places."