The authorty has also taken a lead by demanding that mobile phone companies remove masts that have already been put up at three schools.
The decision comes two weeks after an independent government report into the health effects of transmitters. It advised that masts should be kept away from schools, hospitals and residential areas.
Mark Hunter, chairman of Stockport's education committee, said it was the council's legal duty to care for children while they are in school.
'In the light of new evidence we have decided to make governing bodies aware that we will not support any future applications and would like to see the existing masts taken down as soon as practically possible.'
'I am sure parents will be pleased to see this change and understand that the safety of school children is the council's paramount concern.'