The account, which incorporates Baileys' flagship Irish-cream liqueur brand, is worth £5 million in the UK.
BBH will now be required to develop an advertising campaign to help Diageo grow Baileys world sales, which amount to 6.2 million cases per year.
Chris Harris, the president of international operations at BBH, said: "Winning a new piece of business from an existing client is always the dream scenario. In this case, the brand is a great opportunity for BBH to show its global capabilities. The Baileys brand has been brilliantly built by the team at Diageo so we're looking forward to helping them take it to the next level."
BBH's relationship with Diageo began in 1999 when the agency won the business for the whisky brand Johnnie Walker. A year later, BBH went on to win the Gordon's Gin account.
However, the agency missed an opportunity to increase its presence on the roster after it lost out to Mother in the race for the Archers account last month.
JWT originally won the Baileys business in 1997 after Diageo parted company with the incumbent, Lowe. JWT's final work for the brand will focus on the launch of Baileys Glide - Irish cream blended with vanilla. Despite the loss of Baileys, JWT will continue to work with Diageo on the J&B Whisky and Tanqueray Gin brands, as well as the Smirnoff range.