BBH has yet to be briefed on the details of the project but will handle the advertising for the celebrity dance show.
The BBC reappointed Rainey Kelly Campbell Roalfe/Y&R to its creative account in February.
BBH pitched alongside Abbott Mead Vickers BBDO, Saatchi & Saatchi and Wieden & Kennedy.
During one meeting at BBH’s Kingly Street offices, the BBC marketers were greeted by the entire agency dancing to the Strictly Come Dancing theme tune.
Sources told Campaign at the time that the BBC was impressed with BBH’s ideas and its presentation.
A BBC spokeswoman said: "We occasionally meet with agencies that we may be interested in working with in the future to talk about specialist project-based work, however, we do not comment on individual projects."
BBH declined to comment on the appointment.