Barrett will be responsible for promoting radio advertising among advertisers and agencies. She will report to Siobhan Kenny, the chief executive, and takes up her new role in January.
Barrett, a former editor of Campaign’s sister title Marketing magazine, is currently responsible for the marketing of the JWT brand across Europe.
Kenny said: "Lucy brings the experience and understanding of advertising that we need in promoting radio’s particular value and advantage to potential clients.
"She will add serious strength to the RAB team and we look forward to welcoming her."
Barrett said: "I was happy at JWT and very proud of what I have achieved here, but this opportunity turned my head.
"The medium is moving in a very exciting direction and this gives me the opportunity both to promote and explore the potent combination of advertising and radio."