The work is expected to take 10 weeks.
The properties at 380-394 Princes St and 11 Stafford St are owned by Totara Dunedin Properties and demolition is to be carried out by Scope Group.
Buildings there have been in poor condition for years and dangerous building notices applied at part of the site.
The Dunedin City Council granted consent for their demolition in May.
The consent requires demolition to be followed by construction of replacement buildings within two years.
If this cannot be achieved, a public "pocket park" will be created at the site until redevelopment begins.
The demolition company recently completed work in Rattray St, at the Maclaggan St Warehouse and the University of Otago."Scope Group will take all practical steps to ensure the demolition process creates the least amount of disruption to neighbouring properties," it was stated in a media release.
"Noise will be limited to working hours and vibration will be managed throughout the demolition process.
"Scope Group will also have a comprehensive traffic management plan in place to ensure there is minimum disruption to commuters."
Plans for future site development have yet to be confirmed.
The consent decision commented that the council understood a replacement building or buildings would be constructed in the short-to-medium term.
"The future development need not be a direct replica of the historic architecture, but it should be a sympathetic contemporary design that makes use of traditional materials."
