The development (pictured above) has been created by the independent housebuilder, which originally submitted plans for the scheme in December 2017.
The site was initially granted outline consent for 58 homes, but Backhouse reduced this to allow for more community space.
The scheme will mark the second collaboration between Backhouse and Stirling Prize-winning architects AHMM.
At the centre of the plan is the original hospital foundation stone, which will be made into a piece of public art.
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“Throughout this process we have been aware of the importance of the site to the people of Westbury and worked closely with the council and community groups to create a scheme that reflects the town’s rich history and its ambitions for the future,” said Steve Russell, managing director at Backhouse.
Work has started on the site with the hand removal of the roof due to potential bat roosts.
Following the completion of these works, it will move into the demolition phase, which should be finished in June, with construction works due to start in August.
The first new homes are expected to be ready for sale at the beginning of 2019.