Arena BLM, as the agency will now be known, will become the UK arm of Arena, which was launched five years ago, and has a presence in seven markets, including France, Spain, Portugal and across South America.
Once the buyout is complete, Nick Lockett, a founder of the agency, will step down as chairman. Lockett is expected to offer advice as a consultant, but will relinquish executive responsibility. The rest of the management team will remain in place.
Havas' acquisition of BLM follows interest from several potential buyers, including The Engine Group, the owner of WCRS. Engine and BLM were close to signing a deal last year, only for talks to fall through.
Steve Booth, the BLM Group founder and chief executive, said: "Independence served us well, it was right for a long time, but what's important is how we accelerate growth and step up to the next level."