The building is no longer in use following the relocation in April of the indoor market traders to purpose built cabins as part of the new look city centre market.
City of Wolverhampton Council last month named Urban & Civic as its preferred Westside developer to deliver a £55 million leisure led mixed use scheme.
The demolition of Heantun House is another element in making the 6.4 acre site ready for development.
Contractors will work closely with traders on the nearby market to cause minimal disruption throughout the process.
Cabinet Member for City Economy, Councillor John Reynolds, said: "The demolition of Heantun House is a symbol of real change at the heart of the city, where £992 million investment is either on site or in the pipeline.
"The removal of this dated building will pave the way for dramatic changes on Westside that will boost the city centre for residents and as a visitor attraction.
"Throughout the demolition the nearby market will be open for business as usual and we will continue regular dialogue with the market traders to ensure their needs and those of their customers are met."
Urban & Civic have been handed a 6 month exclusivity period and are further developing their proposal for Westside.
They will deliver a multi screen cinema, restaurants, bars, hotel, multi storey car park, apartments, and public realm, in 2 phases over 5 years, with first phase construction expected to start in early 2018 and complete by early 2020.
It encompasses land between Penn Road Island and Salop Street, including the current School Street and Peel Street car parks and the area around Market Square.
Phase 2 incorporates parts of land between Salop Street and Darlington Street, including the Fold Street car park. Works on this section of the development are likely to be completed in 2022.
- released: Tuesday 23 August, 2016