Parker made seven board-level redundancies last Friday, as Centrica handed control to the AA's new joint owners, venture capitalist groups CVC Capital Partners and Permira.
Parker, who was responsible for marketing turnarounds at Kwik-Fit and Clarks Shoes, will control most of the marketing function. He will also oversee Publishing, AA Ireland and the Driving School.
Director of road services Kerry Richardson has also had his role scrapped.
His deputy, Kerry Cooper, will take on the new role of road sales and marketing director.
Salmon's role will be split on an interim basis between Neale Phillips, who heads AA Insurance, and Lloyd East, who heads Direct Lending.
According to sources close to the AA, Parker does not favour a centralised marketing strategy and wants the AA's operations - road services, insurance and lending - to be run as independent businesses. This has fuelled speculation that the long-term plan is to sell off parts of the business.