In his previous role, which he held since April 2007, Jaye led the overall marketing capability and oversaw the agency's client strategies.
Prior to Digitas, Jaye spent five years at Wunderman as its UK managing director where he co-founded Wunderman Interactive UK and grew the company into a full-service digital marketing agency.
Before Wunderman, Jaye had senior roles with OgilvyOne Worldwide, K2 Design and The Idea Logical Company.
Alexei Orlov, regional president, EME, said: "David brings a wealth of client leadership experience to the region.
"As a seasoned marketing strategist with deep expertise in interactive, he will provide inspired vision to our marketing capability."
Jaye said: "Draftfcb's through-the-line expertise and creative product, coupled with its great client roster and regional reach, are what most excited me about this opportunity.
"I'm really pleased to be back in EME after two intense years abroad and look forward to helping Draftfcb reinforce its position as a leader in interactive."