The New Theatre Royal project will include construction of a creative space for film, television and drama students from the University.
The four-floor extension to the existing building will contain a double-height studio theatre and double-height television studio, each with its own control room.
There will also be six areas that can be used as both teaching rooms and drama studios, plus three music practice rooms and two offices.
A new side entrance, foyer and lift will be shared by both theatregoers and University staff and students. The theatre’s existing entrance will continue to be used as well.
Rob Lipcar, senior project manager at the University, said: “We look forward to the delivery of these splendid facilities, for both the New Theatre Royal and the University, next year.”