Current ground floor tenants of the same Old Hall Street premises, Compton Care, have agreed to vacate the building by 31 March.
This will pave the way for full demolition works to begin in May and complete towards the end of the summer.
As part of the project, a collection of small, vacant buildings in the council's ownership on St George's Parade will also be demolished.
The demolition programme will enable more detailed ground investigations to take place ahead of a full planning application being submitted for the City Learning Quarter development.
The City Learning Quarter will be delivered around the Old Hall Street and St George's Parade area of the city centre.
It will see City of Wolverhampton College relocate its Paget Road campus activities to the location, and will also encompass the college's Metro One Campus, the council's Adult Education Service, and Central Library.
The aim is to improve the offer to all users of the library, college and adult education provision.
The City Learning Quarter will also see investment in the buildings and public realm around them as part of the reimagining of Wolverhampton city centre, which is benefitting from £1 billion of investment.
Councillor John Reynolds, Cabinet Member for City Economy, said: "The City Learning Quarter will sit in a key city centre location and is part of how we are reimagining our city centre.
"It will provide a huge facelift to that area and bring in increased footfall to help boost the local economy.
"It is vital we improve the city's learning, apprenticeship and employment offers to young people and adults in the City of Wolverhampton.
"The City Learning Quarter will provide an inspirational environment for people to learn in and will offer excellent connectivity to the nearby railway station, bus station and tram stops.
"We are working hard with City of Wolverhampton College to ensure we deliver an education hub that will enable education and skills providers, students and residents to flourish and grow together."