Dare Digital, which creates online marketing campaigns, will continue to be run by Collier and majority owned by staff.
The deal will see Dare work across a range of BBH clients. The two companies have already worked together on the launch of Microsoft's Xbox last year, with BBH creating the advertising and Dare Digital building the playmore.com website.
Gwyn Jones, managing director of BBH, said: "We have seen the digital production market develop into an agency rather than production company model. Consequently, it makes sense for us to be able to offer our clients the opportunity to establish retained relationships with a digital partner aligned to the agency. In Dare, we have a partner who shares our approach to business and our obsession with producing great work that works."
Collier left BBH and set up Dare Digital in 2000. It has won awards for its online "stickman" campaign for Yell.com, and its work for Xbox was shortlisted for a Cannes Cyber Lion award this year -- the only digital work from the UK on the shortlist.
Other clients of Dare have included Universal Music, 19 Entertainment and Barclays, also a client of BBH.
BBH also revealed recently that it had bought a stake in the independent Brazilian advertising agency Neogama.
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