The deal, for an undisclosed sum, will see Red folded into the production services company's existing post-house, Smoke & Mirrors.
The merger with Red, which worked on the Orange "gold spot" cinema campaign through Mother, will see staff and equipment move into Smoke & Mirrors' offices on Beak Street.
Tag bought Smoke & Mirrors, which recently worked on the "EA Battlefield" spot for EA Games through Wieden & Kennedy, in 2003. It embarked on a £1 million investment in the company, opening an office in New York and purchasing new equipment for both offices.
Tag's chief executive, Steve Parish, said: " We are really excited about the further expansion of our post-production capability. The two companies complement each other in terms of creative talent, service offering and client base."
The Smoke & Mirrors managing director and chief executive, Penny Verbe, said: "We've been expanding our range of services for some time. With the merger, Smoke & Mirrors will become a full-service facility with a higher capacity for creative work, versioning and delivery."