Lunt will be in charge of developing the agency’s new digital arm, working across all clients.
He joined Leo Burnett five years ago and has worked on campaigns including "#LikeAGirl" for Always, and "we all make the Games" and "Little Piccadilly" for McDonald’s.
Before Leo Burnett, Lunt was the head of hypermedia at GT London, now known as VML.
Juliet Haygarth, the chief executive of BMB, said: "Ben’s really smart and has a bundle of energy. He’s got oodles of varied experience, but he’s uncynical and bursting with ideas. It’s a winning combination."