He replaces Henry Rowe, who left in April this year to launch a digital consultancy. MEC has no immediate plans to replace him.
In his new position, McGee will report to Neil Jones, Carat's managing director.
Jones said: "Charlie has a fantastic reputation in the industry and a great blend of skills. He has strong entrepreneurial nous and is well respected. He was the number-one candidate for the job by a mile; we are very pleased to have him."
McGee joined MEC Interaction as the commercial director in August 2005 from Profero, where he was the head of client services.
He went on to become the managing partner at MEC Interaction, responsible for running the UK digital operation and overseeing a team of 25.
Before joining MEC, McGee also helped establish Inventa, Profero's mobile content arm, working with companies such as Orange and Vodafone, and musicians including Arctic Monkeys and Dizzee Rascal.