The accounts, worth £3.6 million, were awarded without a pitch. The agency won the business on the strength of an earlier project it developed for the biscuit manufacturer, which never aired.
At the end of last year, FCB London was awarded Cadbury's Chocolate Fingers and McCann Erickson London picked up the Jammie Dodgers account after Burton's split with Saatchi & Saatchi. The changes were instigated by the marketing director, Jaspal Chada, who joined in February last year.
Chada said: "BBH has a proven track record. I am looking forward to this partnership exploiting the potential of the UK's favourite chocolate biscuit brand."
One of BBH's first tasks will be to develop work promoting Burton's new range of marshmallows and biscuits under the Cadbury's Highlights hot chocolate brand.
Annicka Locket, the business director at BBH, said: "Cadbury's Fingers are an institution - who wouldn't want to take up that challenge?"