Yannick Bolloré, the chairman and chief executive of the French advertising company, will assume Benett's responsibilities for day-to-day management of the global Havas Worldwide network.
Benett joined Havas Worldwide, then known as Euro RSCG Worldwide, in 2004 as global chief strategy officer and was promoted to global chief executive of Arnold in 2010.
He was then appointed global president Havas Worldwide in 2013 and chief executive of Havas Creative Group in 2014.
Bolloré said: "It's a very exciting time for Havas. We are well on our way to realising our goal of being the most integrated and innovative communications group of our industry.
"I would like to thank Andrew for the fantastic job he has done in implementing our 'Together' strategy and building the organisation to what it is today, as well as the impact he has made throughout Havas over the last 13 years. I wish him all the best in his future endeavours."