He becomes the production company's head of new-business development, a newly created role in which he will investigate fresh areas in which RSA's expertise can be exploited.
These include viral activity and possible future assignments such as the all-star mini movie for BMW by Fallon Minneapolis, which made its UK debut in cinemas earlier this year.
RSA hopes that Gulliman, who starts his new job at the beginning of August, will bring its offering more closely in line with agency demands.
The job grew out of a series of meetings between Gulliman and RSA earlier this year to choose a director for BBH's upcoming television campaign for KFC.
Kai-Lu Hsiung, RSA's managing director, said: "We have a good roster of directors but times are changing and we have to look at how we can address those changes."
She added: "Unlike other production companies, we don't have ex-creatives as directors so we can benefit from Andy's expertise."
Gulliman joined BHH in 1998 from Abbott Mead Vickers BBDO where he had been a producer for three years. At BBH, he was responsible for setting up Mint Source, the agency's new-director reel and music-promo production arm.