New homes are planned for the parcel, which was acquired in 2005 as part of the nationwide Hospital Sites Programme.
Devonshire Homes was appointed to the project by national regeneration agency English Partnerships.
EP area director for the south-west David Warburton said: "Devonshire Homes was selected as the preferred development partner on the basis of their high quality proposals, their approach and their commitment to continuing the engagement with residents and businesses.
"They have proposed a scheme that will deliver a range of affordable and environmentally friendly homes and respond to the historic nature of the sites."
While formal planning approval is yet to be sought, it is expected almost 80 new homes will be built on the 1.4 ha site. They will surround the former hospital buildings, plans for which have yet to be drawn up.