Marquis has been the part-time, non-executive chairman of the agency for the past year, having previously held the roles of managing director, chief executive and chairman. He will sever his links with the agency at the end of March.
ZenithOptimedia does not intend to replace Marquis as chairman.
During his time at the agency, he helped to oversee the merger of Zenith Media and Optimedia, taking the role of chief executive at the merged agency before handing over to Antony Young three years ago.
Marquis will focus on other business interests, including his roles as the chairman of the National Readership Survey, chairman of the Media Circle and a non-executive director at the printing company St Ives.
Steve King, the global chief executive of ZenithOptimedia, said: "Simon's contribution to ZenithOptimedia has been hugely important. He has provided good advice and highly intelligent company. It is to his credit that he leaves with the UK business in its strongest health in years."
Marquis said: "After eight years, it's time to close this chapter. I have enjoyed being part of a great agency and wish it continued success."
Before he joined Zenith Media in 1998, Marquis was an editorial director at Haymarket Publishing. Before that, he was the managing director of Court Burkitt & Company.