In response, Craik Jones has restructured its creative department, and promoted its creative heads, Rebecca Rae and David Brown, to be joint creative directors.
The pair will head the creative department, supported by the agency's co-founder, David Watson, who is stepping down from his position as the chief executive to become a partner. Watson will now be responsible for overseeing the management of the agency's creative operations.
As part of the restructure, Ed Carveth, the Digitas digital creative director, has been hired as creative head with responsibility for digital. He replaces Jonas Lembke, who is leaving the agency after just six months in the role.
Buckingham's arrival at Publicis is the first senior creative hiring since David Prideaux joined as the executive creative director in April.
Prideaux said: "Mark is talented and experienced, and a perfect fit for what we're trying to do at Publicis."
Buckingham's departure comes in the wake of Craik Jones' loss of its flagship Land Rover account to Wunderman. He has won awards for work on the marque, including a D&AD yellow Pencil and a Campaign Direct Silver for the "Bulldog" campaign in 2006. He is a co-founder of the start-up KBH.