It is the first development of its kind in the town, with accommodation specifically targeted at so-called key workers.
Stratford Town Trust owns the current building, and will retain ownership of the land, but the apartments will be owned, managed and maintained by housing association Orbit Housing.
Work is due to be completed in summer 2017.
“This is a key development for Orbit, as it demonstrates our commitment to providing more homes across new and different tenures to meet the needs and aspirations of our customers.
“With the rising cost of homeownership pushing many out of the housing market, we have seen a huge rise in the demand for rented properties. Our new high-quality homes will offer local people a flexible housing option, in a great location.”
Helen Munro, chief executive of Stratford Town Trust, described the development as groundbreaking.
“It is absolutely right that those working hard in our hospitals and schools can afford to live in Stratford. We are confident this development will have a positive impact throughout the town,” she said.
David Austin, of ABD Developments, which is owned by the Bird Group, the Henley Estate Company, and Deeley Properties, all of which are involved in the development, added: “There is an intrinsic need for more key worker accommodation in Stratford, to allow for the people who work in its hospitals, schools and emergency services to live in the town.
“I am sure this development will prove to be extremely popular.”
Warwick House was most recently occupied by Intrum Justitia, a debt collection agency, but for many years previously the land was home to Stratford District Council’s headquarters.
Its redevelopment did cause some controversy when it was first announced lasy tear as the 64 one-bedroom flats and 18 two-bedroom flats will have less than 40 car parking spaces between them, although it is understood people who live there will not be able to apply for residents’ permits for surrounding roads.