Meyers has been at the helm of Millward Brown for 10 years, and he is currently in discussions with Eric Salama, chairman of Millward Brown's holding company Kantar, regarding a new role in the network. He will remain as chairman until the end of 2007.
Salama said: "Under Meyers' leadership MB has innovated and widened its offer, globalised and become a magnet for top talent.
"I very much hope that we will benefit from Bob's talent for years to come."
Campbell's promotion to CEO is effective immediately. She joined the market research company in 2000 as CEO of the North American business group, before progressing to president of global development.
Salama said of Campbell: "She has a great track record in growing client relationships, developing talent and building new capabilities; she knows our industry inside out and knows the importance of each part of the jigsaw that goes to make up a great offer."