Miller, who joins the agency later this year, will report to Darren Bailes, the executive creative director.
His appointment comes four months after the departure of the creative director Steve Vranakis, who left in June to join Google Creative Lab. Bailes, who worked alongside Vranakis, was promoted after his departure.
During his five years at CP&B, Miller was a creative director at the agency's Boulder headquarters. He predominantly worked on the Domino's Pizza account, with his most recent campaign, "show us your pizza", winning awards in Cannes this year.
He also created campaigns for Coke Zero, Volkswagen and Burger King.
Before CP&B, Miller was a senior copywriter at JWT New York.
Bailes said: "Craig brings a wealth of experience from one of the world's best agencies. We're over the moon."