The council last year purchased numbers 1 to 5, which sit near to the Mander Centre car park entrance, and contractors will begin levelling the buildings in the coming months.
The site will be used for car parking in the interim to provide additional revenue income to the council ahead of future marketing of the site for regeneration.
Across the Southside area, the £7.6 million expansion and redevelopment of Casino 36 was completed in November, bringing an extra 100 jobs to the city.
The former Netto building and the old furniture shop at the corner of Snow Hill and Cleveland Street have also been razed to pave the way for the relocation of the city centre market.
Councillor John Reynolds, Cabinet Member for City Economy, said: "Southside is looking very different as we reshape this area of the city.
"The new market will be a real asset and we are developing our strategy for the immediate surrounding area.
"It all fits into the £1 billion of investment that is either on site or in the pipeline for the city centre."
The new city centre market, fronting Cleveland Street, will boast 20 cabins and 48 stalls.
- released: Tuesday 27 June, 2017