At the same time, Kym Douglas, the executive planning director, who was promoted from planning director in June, is leaving the agency without a job to go to.
The moves are the first in a line of changes planned by Neil Simpson, who took over as the chief executive in September.
Simpson said: "The changes will see us refocusing and re-energising the talent in the building." He is yet to decide if Douglas will be replaced.
Quick, who joined Publicis in May 2003, will now take internal management responsibility for the agency, while assisting Simpson in implementing his plans.
Before Publicis, Quick worked at Ogilvy & Mather, where he was a planner; Lowe London, as the worldwide account director on Smirnoff; and Partners BDDH, as the head of client services.
Simpson said: "Neil has proved that he is an excellent operator. I've known him for years, and know that we share the same values and goals."
Quick added: "Publicis is like a rough diamond, and my job will be to shape the agency internally and refocus it."