In their new roles as co-chief executives for the group that manages all Havas Media's interactive assets, de Buruaga and Rhind will focus on client services, product development and new initiatives.
Both senior executives have been promoted after strong track records within Havas Digital, de Buruaga as chief operating officer and Rhind as chief strategy officer.
Epperson, the founder of Hook Media that was acquired by the communications group and subsumed into Havas Digital in 2001, is said to be leaving to pursue "personal projects".
Alfonso Rodes, chief executive of Havas Media, said: "The appointment of two trusted and valued senior executives within Havas Digital is a strong move for us. Under their guidance, Havas Digital has achieved market leading growth, doubling in size every two years.
"Working with Don, both Gabriel and Anthony have helped develop one of the most progressive teams and positive cultures within the industry."
The change in leadership follows seven years of growth for the digital umbrella group, including 40% in like-for-like revenues in 2008. The strong performance is largely attributed to the success of Havas Media's proprietary digital marketing campaign management system, Artemis, in addition to its campaign management system, Adnetik.
Havas Media is no stranger to shared leadership roles, with its largest UK asset Media Planning Group having thrived under joint managing directors Mark Craze and Marc Mendoza until its restructure in November.
Rodes noted: "Joint management structures and teams have worked exceptionally well for us in the group and we are delighted that these dynamic and talented managers will be taking us forward to meet the challenges and leverage the opportunities that this new economic climate will present."