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:
15. Sold
The building last served as a court before closing, at which point it was sold for private redevelopment. Photo: s
16. Closure
After decades of service as the Crown and County Court, it closed in 1992, fell into disrepair Photo: s