Dodd, who only joined MBA six months ago as a managing partner, steps up to replace the current managing director, Graham Monk, who moves to the new role of deputy chairman.
Monk will now be responsible for growing new business and developing existing client relationships. He joined MBA shortly after its launch in 1994 and has been the managing director for the past four years.
As a partner at TBWA, Dodd ran brands including Thomas Cook and PlayStation UK. Before joining there in 2000, he was the marketing director of In Real Life, part of the Chime Group.
Dodd said: "I was employed by MBA as managing partner, and part of the plan if things went well was to become managing director now. The agency wanted fresh blood and my background is very much integration, which is what MBA is all about. I think MBA has gone a little too low profile, it is like a well-kept secret and needs to be put back on the map."
The role of chairman, which is currently held by the creative director, Graham Kerr, remains unchanged.
Stephen Maher, the chief executive of MBA, added: "We are entering 2003 with a management team which will ensure that our agency continues to succeed and maintain a high level of service for our clients."
Last month, TBWA/London yielded the creative account for Le Creuset, the French cookware manufacturer, to MBA.