Kenny, who left HarperCollins in October 2013 after six years, will replace interim CEO Linda Smith, who is a former commercial director of GCap Media.
Smith stepped into the role when Andrew Harrison stepped down from his post in September last year.
Kenny’s brief will be to "reinvigorate RadioCentre, to redefine its purpose in a consolidating industry, and to help shape the future of commercial radio", according to the industry body.
Kenny said: "If I could have designed my perfect job, it would have looked a lot like being CEO of RadioCentre. Radio is a terrific, thriving sector and consumers tend to have a very strong emotional connection with their favourite stations. There will inevitably be challenges, which means there is plenty to do.
"I have been more than impressed with the energy and enthusiasm of the leaders in this industry and I can’t wait to get started."
Prior to Harper Collins she was director of strategy and comms at government department DCMS, working for Secretary of State Tessa Jowell.
She also worked in the Number 10 press office during the tenure of prime ministers John Major and Tony Blair.
Before her time in government she was director of strategic comms for the National Magazine Company and EMEA vice president of comms at Walt Disney TV.
Kenny, who takes up the role on 31 March, is one of a select few comms professionals to reach senior executive positions.
Other examples include John Fallon, the CEO of publishing group Pearson, who started his career as director of comms at the company, and Sue Clarke of brewer SABMiller, who was elevated from her position of corporate affairs director to the post of MD.