Perry, who joined the WPP agency less than a year ago, handed in his notice last week.
He was previously the joint chief executive at Wunderman sister shop Fabric Worldwide.
Perry helped launch Fabric, the WPP-funded big data and platform specialist, as True Worldwide in 2010.
Before this he was the joint chief executive at Razorfish UK.
Earlier in his career, Perry launched DNA Consulting, one of the first UK digital ad agencies, in 1996.
It was acquired by aQuantive, the owner of Razorfish, in 2005. He left Razorfish in 2010 after it was bought by Publicis Groupe.
Mel Edwards, the EMEA chief executive and UK chairman at Wunderman, said: "Perry leaves with the agency’s thanks and best wishes."
Wunderman said that Perry’s replacement will be "announced shortly".