At 57, Haupt has reached his designated retirement age, although his decision is also thought to have been influenced by health issues.
He will remain as the chairman of Publicis Groupe Media, formed last year to include the Publicis media agencies Starcom Mediavest and ZenithOptimedia, in addition to acting as a consultant to the Publicis chairman, Maurice Levy.
"Roger's involvement will be less but he will be an active chairman of PGM," Levy said. "This isn't a token role."
The growing influence of Klues, 50, the Starcom Mediavest chief executive, is reflected in his appointment to Publicis Groupe's "inner cabinet" management board.
"We can't build a strategy for a communications group without taking into account the emerging importance of media and its influence on our holistic approach," Levy added. "Jack is very much at the centre of all that."