Frank said Medley would run a portfolio of consumer clients in addition to his role at Francis.
Graham Goodkind, founder and chairman of Frank, said: "I’ve known Richard for many years and I have tried to hire him before, but for whatever reason it wasn’t the right time or place, so I’m delighted that we’ve got over the line this time.
"Adept at dealing at senior level with clients, providing considered strategic advice, he also has a sharp, creative mind which will play out perfectly here at Frank."
Medley said: "Not many agencies have managed to keep the creative reputation flowing as consistently as the guys at Frank have for the past 15 years. And having been envious of that from the outside, it feels pretty good to be on the inside and contributing to what comes next."
Meanwhile, another board director, David Fraser, is to leave Frank in early April.
Medley left Nexus in November, having joined as managing director in February 2012 from Spider PR, where he was also MD. Before Spider PR he was MD of Publicis Consultants, following senior stints at GCI and Porter Novelli. He has worked in agency PR for more than 20 years.