He said that headteachers, not town halls, would be responsible for the "operational freedom" of schools in the future.
But in his speech this week to two Local Government Association conferences in Newcastle-upon-Tyne, he stressed that local authorities would have a vital role in creating the new joined-up children's services.
Mr Clarke told the representatives that their role would "not for the most part be concerned with providing services", but that it was wrong to predict the death of local government.
"Yes, we have left behind the local authority as the fount of all knowledge and as the controller of all services," he said.
"Your task is to lead the drive for higher standards and better outcomes across the whole children's services agenda."
He said that local authorities would have a new relationship with schools, in which they would act as "advocates" for parents and children, retaining responsibilities for admissions and special needs.
They would be expected to challenge schools to raise standards and promote personalised learning, but they would not have "powers of direction with a capital 'D' ". Under proposals in the Government's five-year plan for education all secondary schools will be able to gain independent foundation status through a simple vote by their governing body.
Mr Clarke revealed that the Government would be publishing plans in December to create foundation partnerships, collegiate groupings of schools, and that he hoped local authorities would learn to work with them.
Alison King, chairman of the LGA's children and young people's board and leader of Norfolk county council, welcomed the speech. "We do not have any difficulty with the prospect of schools being autonomous," she said.
"But we strongly believe that local authorities still have an important strategic and co-ordinating role in children's services. I do not see a complete demise of local authorities."