A total of nine two-bedroom apartments will be built on the former site of Thomas Muir Academy in the East Dunbartonshire town.
The development, just off the town's Wester Cleddens Road, is part of the Bishops Grove development of 40 private homes, which will feature a range of apartment, townhouse and cottage-style properties.
The £1m building contract for the nine apartments has been awarded to Glasgow-based firm Mactaggart and Mickel.
Councillor Ashay Ghai, deputy leader of East Dunbartonshire Council, said: "As convener of the council's Neighbourhood Services Committee I am only too aware of the shortage of affordable homes across the area.
"These nine new homes on the site of the former Thomas Muir Academy will soon be available for rent and therefore go some way to alleviate this problem.
"We are very grateful for the Scottish Government grant funding, which will help towards the cost of purchasing these flats, and we are looking forward to working with Mactaggart and Mickel Contracts, as I am sure they will deliver a high quality product for the council."
Peter Shepherd, director at Mactaggart and Mickel Contracts, said: "We have an abundance of knowledge and experience when it comes to offering value for money whilst upholding the quality expected from our company.
"With 89 years of construction experience and numerous developments delivered in partnership with local authorities, Mactaggart & Mickel Contracts is ideally positioned to provide quality solutions to match our clients' needs whilst addressing the shortage of social housing in Scotland.
"We hope that these affordable homes will make a positive difference to the residents and the East Dunbartonshire area once complete."