He succeeds Mark Lund, the former Delaney Lund Knox Warren chief executive, who quit the role after his appointment to take charge of COI.
McGuinness will operate alongside Penny Hughes, the AA's president and ex-Coca-Cola UK president, and Tim Lefroy, who succeeded Baroness Peta Buscombe as chief executive earlier this year.
McGuinness' appointment comes as the AA strives to maintain the relationship with the Government that was nurtured by Buscombe and to ensure that the body remains properly funded.
Lefroy said: "We must put intellectual authority at the heart of the case for advertising. Andrew shares this vision and will be a powerful advocate."
McGuinness added: "It's never been a more exciting yet a more difficult time for the industry. We need to get back on the front foot. We're very good at advertising product but less good at making our own case."