The deal, worth a reported £20m, will see BLM combine with five-year-old Havas network Arena Media Communications.
The newly merged entity, renamed Arena BLM, will run as a separate business to Havas' Media Planning Group agency.
It will form the UK arm of Arena, which was launched in 2002 and has a presence in seven markets including France, Spain, Portugal and South America.
Steve Booth, who remains chief executive of Arena BLM, said: "Independence has got us to where we are now.
"But from a client perspective, it no longer has quite the same resonance; it's a bit so what? It's all about performance now."
Booth revealed that BLM was first approached by Havas last April. He said: "We've never been in a position where we've had to sell the agency. Last year was our most successful in the 17 years we've been running. But we knew we were ready, if the right partner came along."
The transaction nearly doubles Havas' media presence in the UK. The enlarged operation, together with Havas digital agency Media Contacts, also gives the French group the second-largest digital capacity in the UK.
Nick Lockett, previously chairman of BLM, will step down from an executive position, although he will continue to do project-based work for the agency, including helping to build Bristol-based BLM Clilverd.
Otherwise, BLM's management team remains intact, with the addition of Gareth Nicholls as business director, a new role for the agency.
Nicholls, who worked at OMD for more than seven years, most recently as business director, joins BLM this month. He takes responsibility for marketing and new business across the agency, as well as leading its flagship Domino's Pizza account.
At OMD, Nicholls led a team of 10, servicing clients including PepsiCo UK and Hasbro.
He was also responsible for communications strategy and media implementation.
Within OMD, Nicholls has worked at M2M as the agency's first employee, as well as Manning Gottlieb OMD. Before that, he worked at Walker Media and John Ayling & Associates.
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