Shropshire Council appointed Willmott Dixon under the Scape framework for a £3.4m contract to develop the building into student accommodation.
Plans include converting the six storey Mardol House into studio apartments with kitchenettes and en-suite facilities to house 85 students.
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A lift and ground-floor marketing suite along with a new entranceway will also be developed.
Simon Leadbeater, Managing Director for residential construction in the Midlands, said: " "This project enables us to bring back to life a building that will play a key role in the on-going economic prosperity of the town."
The project is due for completion in September 2015.
(LM)
