Demolition work will start this week on the schools and flats scheme to create the Putney Oasis Academy which will open its doors in September 2016.
The cost of building the school will be largely funded by the sale of land for 24 flats at the northern end of the site, which is currently home to the disused nurses’ accommodation block.
The hospital was closed to patients in 1999. It has remained vacant ever since and was acquired by the council as the site for a new school in 2012.
Durkan is believed to have beaten Galliford Try, Higgins and Rydon to bag the deal.
Education spokesman Cllr Kathy Tracey said: “After 15 years of dereliction this site will now be transformed into a new primary school for the people of Putney.”