The account move was finalised this month after a period of talks and without a competitive pitch.
Out-of-home campaigns for the drinks company will begin in April. The rest of Brown-Forman's planning and buying duties are unaffected and remain with Universal McCann.
The relationship between Kinetic and UM will be similar to the agency's relationship with Bacardi-Martini, with whom Brown-Forman shares some distribution and marketing services.
Kinetic declined to comment. Brown-Forman did not reply in time for publication.