The business, which will be shared between the Publicis-owned network's two offices, covers the European and North American markets. Ogilvy & Mather, the global incumbent, still retains a portion of the Dove Men+Care business.
Dove, which is one of Ogilvy & Mather’s oldest clients, also continues its relationship with the network on its other skincare ranges.
Stacie Bright, Dove global communications director said: "We are currently working with BBH on a project for Dove Men+Care. We collaborate with many different agencies across the Dove portfolio depending on the task or media channel. Ogilvy continues to be a highly valued partner on all aspects of the Dove brand."
The Dove Men+Care range launched in 2010 with a TV ad, which aired during the Super Bowl in the US in February that year.
"The Manthem" spot followed a man from birth through his life.
In the UK, the brand signed a sponsorship deal with the Welsh Rugby Union in May, which led to the Autumn International Series at the Millennium Stadium in Cardiff being renamed the Dove Men Series.
After announcing the sponsorship deal, Paul O’Connor, the brand manager for Dove Men+Care, said that the brand was looking into opportunities for Welsh national players to become brand ambassadors and feature in future TV, press and outdoor ad campaigns.