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.

The vote in the St Louis suburb is the first since the death of Michael Brown last August led to protests.
A federal investigation found racial bias in the Ferguson police department was widespread.
Two-thirds of Ferguson's residents are black and now half the council.
Shortly after the results came out, a video emerged showing an unarmed black man being shot dead by a police officer in South Carolina.
State investigators said the officer, Michael Slager, would be charged with murder after the video showed him firing at Walter Lamer Scott who was running away.
Turnout in Ferguson increased from 12% at the last elections, in 2013, to 29%.
Wesley Bell, who defeated another black candidate in Ferguson's third ward, said: "This community came out in record numbers to make sure our voices were heard.
"When you have a community engaged, the sky is the limit."
A drive by activists to register new voters and encourage previously disenfranchised residents to vote appeared to have paid off.
"People in general want to see change," Ferguson Mayor James Knowles told the Reuters news agency.
Ella Jones defeated another black candidate and two white candidates in Ferguson's first ward to become the first black woman on the council.
Black residents in Ferguson protested for several days last August after Mr Brown was shot dead by St Louis police officer Darren Wilson.
The protests spread nationwide in November when it was announced that Mr Wilson, who has since left the police, would not be charged.
US police have faced severe criticism from rights groups in the wake of Mr Brown's death, with a series of high-profile deaths of unarmed black men in police custody.

The device was towed by a Navy bomb disposal team to a detonation site in the Solent, where a controlled explosion was carried out at 08:45 BST.
Some trains were halted and early ferries were delayed, following the find on Friday afternoon.
Wightlink Ferries said services were now back on schedule.
The train line between Portsmouth and Southsea and Portsmouth Harbour has also re-opened.
A spokesman for Portsmouth's Queen's Harbour Master said: "We worked very hard to make sure the harbour was not closed.
"There were restrictions put in place for public safety and there was a certain amount of disruption to vessels earlier while the torpedo was towed out."
Dredging work is being carried out in Portsmouth harbour to allow the the navy's new 65,000-tonne aircraft carriers to dock.
Three million cubic metres of sea bed is being removed to deepen and widen a 4 mile (7km) channel.
HMS Queen Elizabeth is due to be handed over to the MoD in 2016 ahead of being put into service in 2020.

The 56-year-old ex-Derbyshire skipper leaves his post as club president to take the newly created job.
Graeme Welch left as elite performance director in June, having been appointed following a management revamp in 2014.
"We have not achieved enough success in recent years. We're determined to change this," said Barnett.
"With a strong captain and players technically sound and tactically clued up, we will be in a great position for next season."
Derbyshire finished bottom of Division Two, having failed to win a County Championship match in 2016.
A review of the "cricket pathway to the first XI" was undertaken, with a new coaching structure put in place alongside a "targeted" recruitment drive for experience senior players, which will be funded by savings made by revamping the coaching team.
Barnett will head a smaller backroom staff "streamlined" and aided by player-coaches, who will work "occasionally" with specialised "world class" coaches and cricketers.
The new structure sees the post of first XI support coach and Twenty20 specialist coach created - neither of which have been filled yet.
"The Elite Performance model regrettably has not produced the results that we have been hoping for," Derbyshire chairman Chris Grant told the club website.
"We have been spending over 20% of our overall cricket budget on coaching and this new model will achieve a better balance between our coaching and playing budget."
Three early 19th Century buildings in Reading are to be converted into private homes, under plans published by the University of Reading.
[NEXT_CONCEPT]
Voters in Ferguson, Missouri, where last year an unarmed black teenager was shot dead by police, have tripled the number of African-Americans on the six-member council from one to three.
[NEXT_CONCEPT]
A World War II torpedo has been blown up in the sea off the Isle of Wight after being dragged up from the seabed in Portsmouth Harbour.
[NEXT_CONCEPT]
Former England batsman Kim Barnett has been named Derbyshire director of cricket in the latest coaching restructure at the Division Two club.