Exeter City Council has appointed Bristol-based Wring Group to demolish the old bus and coach station and cafe. Work is expected to begin in January and to take around two months to complete.
The structure will be demolished to concrete slab level but the building foundations will be retained.
Hoardings that are to be erected round the site while work is carried out will remain in place for an unspecified period beyond completion.
The council has struggled to find a demolition contractor for the Bampfylde Street building, which has not been in use since June 2018.
Its closure was put back by several months because of delays in the appointment of a contractor for the construction of the new, adjacent bus station.
Temporary bus and coach stops were positioned nearby, including on Sidwell Street and Cheeke Street, for more than three years until the new station opened in July 2021.
The old bus and coach station is located on part of what is known as the Citypoint redevelopment site, which includes the buildings on Paris Street and Sidwell Street as far as Cheeke Street.
The site is part of the East Gate development zone allocated in the new Exeter Local Plan.
Citypoint was a response to the failure of previous plans dating back to 2015 for an extension of the Princesshay shopping centre across Paris Street.
It was to include a hotel, retail and food outlets, offices, build to rent housing and a new civic centre to enable the council to relocate and redevelop its current offices across the road.
The council proceeded with St Sidwell’s Point leisure centre and the new bus station at a total cost of £57 million but the rest of the site has remained undeveloped. Its future remains uncertain.