Willmott Dixon is understood to have secured the contract to build the council houses with a £24m bid.
The former Hough Side High School site at Hough Top in Swinnow, near Pudsey will be developed with 55 houses and 27 flats in a single block.
Main works are expected to start next month for scheme completion in late 2026.
The proposed two-storey brick houses will be a mixture of two, three and four bedrooms.
Each house will have its own parking spaces and private garden space.
The proposed three-storey apartment block will contain a mixture of one and two-bedroom units.
Around 350 new homes have been built via the Council Housing Growth Programme since 2018.
