She replaces Martin Nieri, who left CMW in June to take up the chief executive position at Partners Andrews Aldridge.
Wilson has been at Albion for four years, having joined as its client services director before rising to commercial director, then managing director and, finally, managing partner.
Before joining Albion, Wilson worked at Euro RSCG, TBWA\London, Lowe and Brandhouse.
Wilson is set to join CMW, which has clients including Cadbury and Peugeot, later this year.
She said that she took the offer as it was a "big job and a big opportunity. CMW is at an interesting stage of its development. I am keen to build the agency's integrated offer even further, while harnessing its very strong data capability - which is a real differentiator and an area of expertise that is increasingly on the client agenda."
Peter Reid, the group chief executive of Media Square, CMW's parent company, said: "Liz has exactly the right credentials to lead CMW on to the next stage of its development, including potential international expansion. She has big agency experience and has also led international business and teams.
"Liz gets the big strategic picture as well as the detail of operational issues. She has an entrepreneurial drive and hunger that will serve CMW well commercially and prove an excellent cultural fit."