The merger, which adds Triangle's experience in retail marketing to Arc's direct, digital, promotional and experiential offering, creates an agency with around 215 staff. Around ten staff face redundancy.
Mike Spicer, the managing director of Arc, will lead the combined operation with Diana Cawley, the Triangle managing director, becoming his deputy.
They will report to Bruce Haines, Leo Burnett's chief executive.
The decision to combine the two agencies comes weeks after the two used a combined team to pitch successfully for the Post Office's in-branch account. The agency joined Joshua and Publicis on the Post Office roster.
Andrew Edwards, the president of Arc in Europe, the Middle East and Africa, said: "Arc UK was already the biggest player of our offices across the region, and now, with the roll-in of Triangle's talent, it's my belief that this places us in a second-to-none position in the UK market, particularly in the context of our retail expertise."
Spicer added: "The merger will bolster Arc's retail and promotional expertise at a time when the market is demanding such specialist knowledge. Together, we know that we have a very strong offering, as Triangle/Arc Group's recent success with the Post Office account win underlines."