Cook will run the merged London agencies, but will report to Burnett's group chief executive, Bruce Haines. However, it remains unclear who will form his management team.
Cook's role comes after Publicis decided to lose the D'Arcy brand and fold its business into the group's three other networks - Burnett, Saatchi & Saatchi and Publicis - after its $3 billion acquisition of Bcom3.
He is seen to be crucial to the merged agency's relationship with domestic clients, particularly COI Communications. It is thought that D'Arcy's planning director, John Poorta, also key to the £30 million COI account, will take a role. However, it is still unclear whether the creative director, Nick Hastings, will join Burnett. Luca Lindner, the president and chief executive of D'Arcy's Europe, Middle East and Africa operations, is in discussions about an alternative role.
Haines said: "Barry will provide welcome talent and experience to Burnett's management team and we are looking forward to working with him. He and I share the same management ethos absolutely - we have a strong desire to look after clients and, consequently, our staff."
Publicis' chairman, Maurice Levy, will not be drawn on job losses, although he has admitted some are inevitable. A statement from Publicis said: "Haines and Cook have pledged themselves to work hard and fast to minimise disruption to clients. Clients have been assured key members of their agency team will be offered jobs with Burnett."