The building, which was constructed in 1810 to house the court of quarter sessions, is steeped in history.
It was extended between 1849 and 1850, and in the 1880s and later served as the Crown Court and as a County Court, eventually closing in 1992.
It has since stood derelict until it was sold to private developer, Rushbond.
Planned work includes creating an events space within the former main number one courtroom.
Elsewhere in the building, a restaurant, cafe and studio spaces will be provided, along with a new entrance and landscaped public terrace.
A neon art installation, by Turner Prize-winner Martin Creed, will also be permanently put in place on the outside of the building.
The project is expected to be completed by summer next year.
Take a look inside the old building:
2. Court
The courthouse was built in 1810 and later extended but has been derelict since it closed in 1992. Photo: s
3. History
The 215-year-old site on Wood Street is being converted into a multi-use arts venue to include a food hall, offices, events space and studios. Photo: s
4. Derelict
Last month, Yorkshire-based developer Rushbond was granted planning permission for the renovation of the Grade II*-listed building. Photo: s