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Pora, who has spent more than 20 years behind bars for the 1992 rape and murder of Susan Burdett in Auckland, filed the application in August through his lawyer Jonathan Krebs.
Mr Krebs told APNZ he found out the appeal had been allowed early on Wednesday morning but because the news was embargoed he was unable to tell Pora until this morning.
"He was absolutely ecstatic," Mr Krebs said. "He's waited a long time. He did the natural reaction of pumping the air with his fist and said it was awesome and said thank you."
The Judicial Committee of the Privy Council announced overnight that the appeal would be heard during the Northern Hemisphere autumn with the precise dates to be confirmed.
Its statement said the committee had to decide whether it should admit and consider fresh evidence raised by the appellant, and whether a substantial miscarriage of justice was caused by the failure of the appellant's counsel to raise material points at trial and/or in the Court of Appeal.
Mr Krebs said the Privy Council had indicated the hearing would be held in October but he would be applying for it to happen sooner, "simply for the fact that Teina's been in custody for so long".
Pora's legal team raised five grounds for appeal, said Mr Krebs, who is working on the case for free.
Two were accepted - one relating to the safety of Pora's confession and the other around a specific piece of evidence relating to serial rapist Malcolm Rewa.
"The confession was central to the prosecution case but we believe it was a false confession and all of the circumstances of the confession - the way it was obtained and special features relating to Teina - are all grounds which go to our argument.
"The second ground is a very narrow point relating to a feature of Malcolm Rewa's offending. Malcolm Rewa has been convicted of raping Susan Burdett but the evidence we want the Privy Council to consider was not allowed to be given at Teina's trial. It is evidence that suggests it was unlikely that Rewa would ever have had a second person present."
One of the grounds for appeal turned down by the Privy Council also related to Rewa, another related to a pair of ear-rings and a third related to the relationship between a couple of gangs. The two grounds that were accepted were the most important, Mr Krebs said.
Pora was convicted in June 1994 as a party to the rape and murder of Ms Burdett on the basis of confessions.
In 1995, DNA evidence linked the attack on Ms Burdett to Mr Rewa. Mr Rewa was eventually convicted of the rape of 27 women, including Ms Burdett.
In 1999, the Court of Appeal quashed Pora's convictions as a result of the DNA evidence implicating Mr Rewa and evidence that Mr Rewa's acted alone.
The appellant was convicted again at his retrial in 2000 and his appeal to the Court of Appeal was dismissed.
The Privy Council said the judgment would almost certainly be reserved.
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