The authority is scrapping all of its traditional departments over the next three years and introducing a neighbourhood structure, supported by core central services.
The city is being split into three areas - north, south and central - and will be run locally by joint service teams. Initially, each area will have its own head of education. Existing directors are bidding to head 10 new corporate remits but the number of posts could be cut to six within three years.
Chief executive Douglas Paterson described the reforms as "a sensible and reasoned approach to change". He added that teachers were already being asked to deliver "joined up services" with social workers and health professionals, and pledged that the council would continue to respect statutory education responsibilities and the interests of teachers.