The deal is pending approval from the Israeli government's Anti-Trust Authority.
Geller-Nessis works with local and international clients, including Procter & Gamble, and is a full-service agency offering traditional advertising as well as interactive, online and direct marketing.
Tom Bernadin, the chairman and chief executive of Leo Burnett Worldwide, said: "This move enables us to expand our presence in Israel. We see Geller Nessis as a key partner because its capabilities mirror Leo Burnett and Arc's so closely."
Publicis Groupe already has a strong presence in the Israeli advertising market through Publicis Ariely and Saatchi & Saatchi BBR.