The company's advertising has traditionally been handled in-house.
The Miami-based agency's first campaign for the business is expected to launch in March next year. It will include TV, print and in-store components.
Jeff Hicks, the chief executive of Crispin Porter & Bogusky, said: "We're very excited to be working on the Geek Squad business. It's a powerful brand with amazing growth potential."
Geek Squad was founded in Minneapolis 12 years ago, and was acquired by Best Buy in 2002.