The two agencies were shortlisted for the business after Lever Faberge called a review earlier this year. BBH's claim to a place on the list was aided by the work it has done on Lever Faberge's Lynx and Impulse brands.
The pitch was conducted between the two agencies' New York offices. No-one at McCann was available for comment as Campaign went to press.
McCann's New York office is now expected to take even more control of the account than before, with campaigns being produced in the US and adapted for the UK market.
Vaseline has two main brands: Vaseline Intensive Care lotion and the Petroleum Jelly range. The former was the tenth fastest-growing brand in the UK personal care market in 2001, according to Nielsen Media Research.