Bob Jeffrey, the worldwide chief executive at JWT, announced the news on Friday in an all-staff internal e-mail.
He said: "Craig and the executive management team remain focused on the tasks at hand, delivering breakthrough work for our clients. For right now, we need to remain focused as ever on best-in-class ideas and executions."
JWT is seeking a successor and Davis will remain with the network until an appointment is made to "ensure a smooth transition".
The creative assumed the then newly-created post of worldwide chief creative officer in January 2005, after a year of leading JWT's creative efforts across Europe, the Middle East and Africa.
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