Potter, the global business director for the Diamond Trading Company, takes over from Tim Davis. His role at the agency, once a six-month handover is completed, has yet to be decided.
Operating out of JWT's London office, Potter will absorb responsibility for the household and personal care brands in February, with food brands following later in the year.
Bob Jeffrey, the chief executive of JWT, said: "As a valued member of my executive committee and chair of JWT's global business community, Carol is a key driver behind JWT's ongoing transformation into a creative-driven network known for its strategy and breakthrough ideas."
JWT's relationship with Unilever goes back 102 years, servicing household brands such as Sunsilk, Lipton and Persil.