IPG's McCann Erickson network handles the brand in all markets apart from the US, where it is held by WPP's JWT.
The brand currently spends £4 million a year through McCann's London office.
The move will strengthen further BBH's relationship with Unilever. Vaseline brings BBH's total Unilever billings to more than $350 million and is the agency's third global piece of Unilever business - it also handles Surf and Lynx. BBH's New York office will lead the account.
Simon Sherwood, the worldwide chief operating officer of BBH, said: "Skincare is a huge and dynamic market, and Vaseline is one of the great brands, so we are delighted".
Steve Miles, the Vaseline global brand vice-president at Unilever, said: "We decided to rationalise our agency alignments on Vaseline by moving to a single global partner.
"This is no reflection on the work JWT and McCann have done for us in the past, but I'm now looking to the future and am excited about the prospect of working with BBH."