Wright will oversee all of the agency's accounts, which include Peugeot, M&S, Cadbury and the COI.
She has 20 years' experience in the direct and integrated sector and joins CMW from Proximity London, where she held the role of managing partner and ran the European account for Intercontinental Hotels Group.
Martin Nieri, managing director of CMW, said: "Claire has experience of working with some of the world's biggest names under her belt and is a real expert in the world of CRM.
"She will be working closely with all of our clients to add greater value to their business and explore new strategic directions for their communications."
Prior to her two years at Proximity, Wright was client services director at Draft London, working on the Post Office and Telewest Business accounts.
She also worked at OgilvyOne Worldwide where she ran the American Express membership rewards programme across Europe.
Wright said: "CMW puts the clients' business requirements at the heart of what they do and produce outstanding creative work to meet these needs.
"As well as that, CMW is a growing business with a great client list and I am pleased and excited to be joining the agency."