Cairns, who is also a former head of account management at TBWA/London and group account director at Taxi, New York and Clemenger BBDO, Melbourne, left the independent Inferno in January.
He was responsible for integrating Farm into the business in February 2012 after Cello pulled the plug on the Farm as well as winning the Legal & General ad account and the NSPCC.
Cairns said: "I think perhaps everyone in advertising has probably dreamed about working at BBH at some stage in their careers. Joining the esteemed ranks of people in Kingly Street is both exciting and intimidating in equal measure. I can't wait to get started."