The agency has been briefed to promote Diageo's Gordon's, Smirnoff, Baileys and Bell's spirit brands.
Adam & Eve, which also works on the Bell's whisky brand, won the business after a competitive pitch against undisclosed agencies.
This is the second time that Diageo has run a multi-brand campaign. In the summer, it launched a similar campaign created by Saatchi & Saatchi X, the retail marketing arm of the Publicis advertising group.
The integrated brief covers advertising, online and in-store activity.
Diageo has said it will spend £47 million on marketing its alcohol brands in the run-up to Christmas and the new year, prompted by a better-than-expected performance last Christmas, when sales in the spirits category grew by 6 per cent. It has also promised to improve the visibility of its brands in-store.
Diageo plans to launch activity for its individual brands as well, and is currently running a TV campaign for Baileys by Bartle Bogle Hegarty.
The global "birthday candle" campaign is designed to remind consumers of the joy of spontaneous moments with friends. It is the first from BBH since it won the Baileys advertising account in June.