Final approval is subject to Communities and Local Government Secretary Ruth Kelly deciding whether to ‘call in’ the application.
More than 17,000 people objected to the incinerator.
Veolia hopes the plant will be operating by 2010, processing some 210,000 tonnes of waste per year and producing 16.5 megawatts of electricity.
The facility was granted a pollution prevention and control permit by the Environment Agency in 2006.
The councils plan to increase the recycling and composting rate to 30% by 2008/09 and just 33% by 2015/16.
As well as the incinerator, four waste transfer stations, a materials recovery facility and a 45,000-tonne capacity in-vessel composting plant are planned.
All the sites have been financed through government private finance initiative (PFI) funding.