Secondary glazing is to be put in homes that used to be part of Roundway Hospital, reports Wiltshire's Gazette & Herald.
The decision came after a planning inspector overruled the Kennet District Council's prior decision in 2004 not to install the glazing.
Planning inspector John Millard approved the appeal that was brought by the Sarsen Housing Association.
Mr Millard told the paper: "The installations [of secondary glazing] would be reversible and would cause no permanent damage to the historic fabric.
"I consider that they would not detract from the character or appearance of the buildings but would preserve their special architectural and historic interest."
Though double glazed windows are not allowed by the government in most buildings of historical significance, installing secondary glazing by way of an inner frame is permissible, he said.
Wiltshire is known for having a range of historic architecture including several manor houses form the 14th and 15th centuries.
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