The agency pitched against incumbent Bartle Bogle Hegarty and Leo Burnett for the business. Fallon was eliminated at an earlier stage of the pitch. BBH continues as the global agency for Johnnie Walker and JWT already has global responsibility for Smirnoff.
Sharon Keith, global brand director for Bailieys, was in charge of the review.
The hiring follows the appointment of Agency Republic to the digital creative account and is the latest in a string of appointments by Diageo.
Baileys is currently running a press advertising campaign aimed at moving it from being seen as a drink consumed only at Christmas.