Cowpe replaces John Hooper, who steps down from the role after five years, and joins Clive Mishon, the other non-executive director on the agency's board.
Marc Nohr, a managing partner at Kitcatt Nohr, said: "We're confident that with Cowpe as the new boy on the board and Mishon remaining to provide consistency, we've found the right balance of skills to take the agency forward."
Cowpe began his career in advertising at BMP in 1972. He rose through the ranks of the agency, finally taking the role of joint managing director and chief executive in 1999.
During his time at the agency, Cowpe worked across a range of blue-chip clients including Barclaycard and Johnson & Johnson.
Since leaving DDB London in 2004, Cowpe has being working as a consultant. He also co-founded The Caffeine Partnership, which advises companies and individuals on how to achieve business growth.