It is hoped the theatre, founded in 1875, will be used for theatrical performances, cinema screenings, comedy and live music.
The BBC studios, at the eastern end of the Palace, will also be repaired and refurbished.
If successful in raising funds it is hoped the theatre will reopen in 2018.
The theatre and studios form part of a larger east wing restoration project to transform Alexandra Palace into a new cultural destination.
As part of the renovations, the glazed east court will become a space for the public and for exhibitions.
Heritage Lottery Fund (HLF) is contributing £18.8m towards the project, while Haringey Council is contributing £6.8m.
The entire east wing will be refurbished at a cost of £26.6m.
Alexandra Park and Palace Charitable Trust have committed to raising the final £1m by summer 2017.
The theatre, which has languished unused for decades, still has much of its original decor and stage machinery in place.
It was created to showcase opera, musicals, plays and all kinds of entertainment, even hosting early cinema screenings.

David Mackintosh was the leader of Northampton Borough Council when the authority authorised the loan to Northampton Town in 2013.
The money has never been paid and the council is in the process of trying to get it back.
Mr Mackintosh said "due diligence was carried out" before the loan was granted.
The Conservative MP for Northampton South said he felt "angry, frustrated and upset" about the ongoing financial problems at the Cobblers.
The club currently faces a winding-up petition from HM Revenue & Customs (HMRC) over £166,000. This is due to be heard on 16 November.
The £10.25m loan was originally given to the club for the re-development of its Sixfields stadium.
Mr Mackintosh said all decisions over the loan were taken at the borough council's cabinet and followed "a lot of work" by officers.
He said safeguards were put in place and were now being deployed by the council to recover the money.
Mr Mackintosh said: "Clearly as leader I have to take some responsibility for what happened.
"It is very frustrating because at the same time there are other things that haven't happened at the club.
"There are serious questions to be answered."
Club chairman David Cardoza previously told the BBC he expected the loan issue to be resolved by the end of last month.
Alexandra Palace has started a £1m fundraising campaign to bring its Victorian theatre back to life after lying unused for 80 years.
[NEXT_CONCEPT]
An MP says he "has to take some responsibility" over an unpaid £10.25m loan to a football club.