The agency won the business after a pitch against undisclosed Cadbury roster agencies, and will now be responsible for developing an online strategy to help promote the Trebor range.
CMW will work closely with Trebor's ad agency Fallon on the business. PHD handles media planning and buying.
The digital work will aim to develop Fallon's "mint people" positioning, which was introduced last summer as part of a £2.5m TV and outdoor campaign to promote the launch of Trebor Extra Strong Gum.
The work included a TV ad that featured a trainee at Trebor coming up with an idea for a new mint gum during a press conference.
Cadbury also invested heavily in developing the other products in its Trebor portfolio last year, which included the redesign of the packaging for its Extra Strong mints and Softmints products.