His departure follows the loss of the £47 million Vodafone UK account to Bartle Bogle Hegarty in December. Dunn was the lead creative on the account.
The JWT chief executive, Alison Burns, said: "Steve is a notable talent and is widely renowned for the quality of his visual sensibility. I think he'll be in very high demand."
Dunn's exit is the latest in a number of senior creative changes at JWT. In January, Nick Bell was forced to relinquish his position as the executive creative director.
Last month, the JWT creative director, Charity Charity, left to join Euro RSCG London, where she will work alongside Mark Fiddes as the joint worldwide creative director on the agency's Reckitt Benckiser account. She previously worked on JWT's share of the FMCG giant's business.
Dunn joined JWT in July 2005 after three years spent working as a commercials director and a freelance art director. Previously, he was the executive creative director at Ogilvy & Mather, a position he lost in 2002.
JWT lost its Vodafone business after it was forced to repitch for the UK portion of the account in October.