The agency said it had tried to head off Roddy's departure, but creative differences had put paid to efforts to keep him at the agency.
His departure follows the promotion of the BBH New York managing director, Greg Andersen, to chief executive earlier this year.
Andersen replaced Emma Cookson who took on the new role of chairman in order to allow her to spend more time working on the agency's £270m Cadillac account.
In a statement John Hegarty, chairman and worldwide creative director, said: "I have a huge respect for Kevin but ultimately we disagreed over the creative direction of the office and Kevin resigned. I'm very sad it came to this.
"I worked hard to avoid this situation but in a company so focused on creativity these things happen."
Roddy joined BBH in 2004 from Euro RSCG New York where he was executive creative director.