Gresham Road SEN school will have a floor area of 8,500m2 over three storeys. It has been designed by Pick Everard.
It will be built on part of what used to be the London Transport Sports Ground in Osterley, which was bought by the council in 2001.
The school will accommodate up to 224 pupils with severe and multiple learning difficulties
Construction starts this summer and is expected to take 30 months to complete.
Separately, Hounslow council has also handed a £9.8m contract to Neilcott Construction for its Wellington Primary School new build project.