Freud is understood to have paid a negligible amount for the agency.
Under the terms of the deal, DFGW will be absorbed into Freud and will move its 12-strong team from London's High Holborn to Freud's offices in Mortimer Street. The agency will trade as Freud Communications, with the name DFGW dropped.
Tom Vick and Hugh Cameron, the joint MDs, will retain management positions in the new unit, as will Dave Waters, the creative director and DFGW's only remaining founder. All three are expected to be given board-level positions within Freud.
The deal means Freud, which has clients including Volkswagen, Coca-Cola and Nike, can extend its services to include advertising, film and branded entertainment.
DFGW's existing advertising clients - Expedia, COI and the charity trust Nuffield - will follow the agency to Freud.
DFGW has held talks with numerous potential buyers over the years, more recently including Lowe London and Saatchi & Saatchi.
Net assets were valued at £1.2 million in 2005.