They are being constructed in the New Zealand Loan and Mercantile heritage building in Thomas Burns St and will be run by the Salvation Army.
Each will have about 50sqm of space and there will also be a community space and a room described as an area for craft-type activities.
Tenants will come from the Government’s housing register.
Private apartments are also being created within the building.
Rates relief will apply to the portion of the project that is about social housing.
The social housing units are to be leased to the Salvation Army for an initial period of 15 years.
Mr Lund said the Dunedin City Council had been supportive under both the mayoralty of Mr Radich and his predecessor, Aaron Hawkins.
"Our aim is to provide the best community housing in New Zealand," Mr Lund said.
Original building materials had been recycled.
Salvation Army social housing national director Greg Foster said the development, backed by the Ministry of Housing and Urban Development, was unusual in that it involved use of a heritage building.
A Salvation Army media release said the social-housing component would be on one floor of the mixed-use heritage building. Market-rate apartments would occupy the upper floors and commercial users the ground floor.
Twenty-eight of the community housing units will be one-bedroom units and one a two-bedroom and another a three-bedroom unit.
The building has been strengthened to withstand earthquakes.
It was constructed from 1872 and began as Otago Wool Stores for stock and station agents Driver Stewart and Co. Uses over the years have included offices, warehousing, an air-raid shelter, and the upper storey was let to clothing manufacturer Sew Hoy and Sons, Heritage New Zealand information stated.
Indoor karting was added in 1991.
The New Zealand Loan and Mercantile Agency Co, which provided investments and loans for trade and commerce in New Zealand and Australia, occupied the building until the 1960s, when the business ceased operations.
Australian architect Prof Robert Morris-Nunn, of Circa Morris-Nunn Chua in Tasmania, has helped to design the project.
"I sincerely hope that the architecture and the real sense of community which will be created by the Salvation Army will greatly enrich the quality of the lives of people who will soon call the L&M home."
