The listed properties on London Road were last used by the Witan International College 10 years ago.
The university, which owns the buildings, and a private developer plan to convert them into 53 apartments.
Christopher Reeve of the university said the buildings "create a sense of heritage" in the town.
If planning permission is granted by Reading Borough Council, restoration work will start in early 2016 and is expected to take approximately nine months.
Three early 19th Century buildings in Reading are to be converted into private homes, under plans published by the University of Reading.