The council plans to knock down the newer school buildings at the site, describing it as "strategically important".
The college, off King Street, closed its doors in 2018 when it merged with the Telford College of Arts and Technology (TCAT) to create Telford College.
The council plans to leave the Edwardian school building, which has been granted Grade II Listed status, intact while the newer school buildings and a bridge link are demolished.
Demolition will take place in phases, the first being the demolition of the buildings immediately behind the original school building.
Work is due to start later in 2020 and a mixed use development of the site is being considered.
Councillor David Wright, the council’s cabinet member for economy, housing, transport and infrastructure said: “The redevelopment of the former New College site will provide a great opportunity to bring new investment into Wellington.
“We are talking to a range of partners about the future of the site and we are fully committed to protecting the listed building on the frontage.”
The former New College site is seen as strategically important for the future social and economic prosperity of the centre of Wellington.