The final round of pitches included Publicis Groupe's Saatchi & Saatchi in New York and WPP Group's Young & Rubicam in Chicago.
The business was previously handled by MDC Partners' Miami-based Crispin Porter + Bogusky, which parted ways with Miller earlier this year. Crispin Porter created "man laws" a spot starring Burt Reynolds for Miller Lite. However, this failed to lift sales.
Randy Ransom, chief marketing officer at Miller, said: "BBH demonstrated great insight into the character of our brand and our core consumers.
"They have shown an ability to work collaboratively and to engage our consumers creatively. They are passionate about the beer business."
Gwyn Jones, chief executive of BBH in New York, said: "We love Miller's 'able challenger' approach and know that we will create engaging work that will help fuel the momentum behind Miller Lite, one of the best brands of the past 30 years."
Although BBH picks up the bulk of Miller's creative duties, the company's Miller High Life brand is still up for grabs.
Miller said it would award duties on High Life, the company's oldest lager brand, considered to be the forerunner of the modern American lager beers, next week.