Construction will start on site in the Dringhouses village area of the city later this year and is scheduled for completion in the early part of 2021.
The £7m project will provide 30 new apartments for people with visual and sensory impairments and other disabilities.
Alongside the new apartments will be a Living and Learning centre that will be open to the local community.
Construction will create jobs for local workers as well as offer work experience placements for local students.
Chris Birch, Chairman at William Birch & Sons Ltd said: “Our team take great pride in their work and they will work closely with the Trust to realise their exciting plans.
“Our team’s expertise coupled with local employment and engagement with many local businesses will bring wider benefits to the city of York and its people.”