Rasmussen joins from R/GA, where he was the executive creative director on the agency's Nike account.
Before R/GA, Rasmussen worked as a creative director on Jet Blue at JWT in New York, and as a creative at Wieden & Kennedy, working on accounts including Coke, ESPN and Brand Jordan.
Rasmussen said: "When I started to explore BBH's recent work, I was amazed. They are a tight team with incredible insight and vision."