BMB picked up the business after a pitch run through Ingenuity. Karmarama, M&C Saatchi and Crispin Porter & Bogusky were involved in the review. The account moves from Publicis London.
George Johnston, the marketing director at KP Snacks, said: "We are excited about the energy, enthusiasm and creative spirit of the BMB team."
A spokeswoman for KP Snacks, which was bought by the German company Intersnack last year, confirmed it plans to spend £10 million on brand marketing in the coming year.
A separate pitch to find a digital agency is ongoing.