The moves were announced by representatives at both Publicis and JWT.
Publicis said the split with the office supply retailer occurred because of differences of opinion about the "nature and scope" of work.
The account is moving to the Chicago office of J. Walter Thompson, a spokesman for the agency said.
Office Max spent $42.3 million on measured media in 2002, according to TNS Media Intelligence/CMR.
The Shaker Heights, Ohio-based retailer was not immediately available for comment. Its the No. 3 office supply superstore chain in the U.S. behind Staples and Office Depot.
Publicis' most recent work for Office Max featured the tagline "Max means more."