He will join Jonathan Rigby, the newly arrived managing director, and Al Young, signed from HHCL/Red Cell as the creative chief, in the triumvirate that will run the agency.
The restructure, initiated by John Banks, BHO's chairman and chief executive earlier this year, is aimed at building the agency's relatively low profile and making it a more potent competitor for new business.
One of the first tasks for Bain, who was the global planning director at Fallon on its Timberland business, will be to introduce a new system under which BHO's four planners will sit alongside creatives and work more closely together.
Bain, 34, began his agency career at J. Walter Thompson in 1997 after an academic career as a cultural anthropologist. His responsibilities included Smirnoff and Kellogg, on which he became board planner.
He joined Fallon in London at the beginning of 2001, moving a year later to the agency's New York office. There he worked on accounts including Starbucks, Sports Illustrated and Timberland. He returned to the UK in May.
Robert Senior, one of the partners at Fallon, said: "He's a smashing bloke. I think he's brilliant."
Bain said: "I hadn't been looking for a move and BHO's offer came out of the blue. Going to a sharply focused agency with an already established distinctive culture didn't seem a particularly interesting thing to do. At BHO, there's a chance to be part of something new."
Rigby and Young worked together on Bain's selection. "Al is an effervescent thinker who seems to have more ideas in a minute than most people have in a day," Bain added.
Rigby said: "David's role will be to take our strategic thinking into surprising and interesting places. What's more, he benefits highly from having worked on both sides of the Atlantic."
BHO, whose clients include Weetabix and Waitrose, hopes the new structure will strengthen it against rival younger agencies.