Gulliman - best known for his work on the award-winning "odyssey" spot for Levi's and Microsoft's Xbox campaign - replaces Mark Hanrahan. Hanrahan announced in July that he was to leave Saatchis after 13 years as a Charlotte Street staffer.
The position had been expected to be filled by Sally-Ann Dale, who currently shares the deputy head of TV role with Manuela Franzini.
The appointment is part of efforts by Tony Granger, the agency's newly arrived executive creative director, to re-energise the creative department with young blood.
Gulliman left BBH in July and spent a brief stint in the newly created role of head of new business at RSA.
"Andy is exactly what we have been looking for. He brings a wealth of creative experience to the department," Granger said.