The switch is a prelude to the drinks giant putting more spend behind new Smirnoff-branded products and less to support the youth-oriented Smirnoff Ice.
JWT takes back the Smirnoff Ice account, along with Smirnoff Ice Triple Black, Smirnoff Twisted V and Smirnoff Raw Tea in the US.
Diageo said the change had been precipitated by a review of its agency conflict policy. Reassigning the business will allow BBH to continue to work with InBev, although the agency will continue to handle creative work for Diageo's Johnnie Walker and Baileys Original Irish Cream brands.
JWT, which already handles Smirnoff Red, will split the enlarged account between its London and New York offices.
James Thompson, Diageo's president, global marketing, white spirits and ready-to-drink, said: "JWT's work has been integral to helping us drive Smirnoff vodka to become the number-one premium spirit in the world."
Smirnoff Ice is believed to have had a tough time sustaining its success in the faddish, competitive youth market. BBH's work for the brand focused on an eccentric Russian, Uri, and his best friend, Gorb.
JWT, which has spent the past 18 months focusing on higher creative standards, has a recent record of award-winning work on Smirnoff Red, having picked up two silvers and a bronze at Cannes during the past two years.
"The spend on Smirnoff Ice may go down, but this will be compensated by spending on a number of new brand extensions," an industry source said.
If you have an opinion on this or any other issue raised on Brand Republic, join the debate in the Forum.