The work had been handled by Crispin Porter & Bogusky in Miami before the agency parted company with Miller earlier this year.
BBH was given the nod ahead of Saatchi & Saatchi New York and Young & Rubicam in Chicago.
Randy Ransom, the Miller chief marketing officer, cited BBH's "great insight into the character of our brand and our core consumers".
Gwyn Jones, the chief executive of BBH in New York, said: "We love Miller Lite's approach and will create engaging work for the brand."