Perry will report to Edwards, who was promoted to EMEA chief executive and UK chairman last month.
His remit will include "taking the UK agency forward", focusing on current clients, including GlaxoSmithKline and News UK, and driving new business.
Perry helped launch Fabric, the WPP-funded big data and platform specialist, as True Worldwide in 2010.
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.
Perry began his career as a media planner at Ogilvy & Mather in 1994.
Edwards said: "Chris has a fantastic pedigree, having worked and run some of the industry’s top agencies. Not only does he bring a new skillset to the business, he’s a really nice guy and I’m looking forward to working with him."
Perry said: "Wunderman is one of the most well-known data-driven creative agencies – not only in the UK but globally. Under Mel’s leadership, the agency has gone from strength to strength in the UK and I cannot wait to take on the responsibility of helping drive the business to the next level."
Neil Miller, the other joint chief executive at Fabric, joined Possible, the WPP-owned digital agency, as its UK chief executive in February.