The parties in New Zealand were notified this morning.
Crown and defence had filed submissions last week on whether Mr Pora should be tried for a third time of the 1992 crimes.
Parties received a draft order on Monday morning recommending Pora not be retried.
Mr Pora was convicted of her rape and murder in 1994 and again in 2000.
Mr Pora was released on parole after spending 21 years in jail.
Malcom Rewa was convicted of her rape in 1998 after DNA from semen was linked to him. But two juries could not reach a decision on whether he murdered her.
Rewa is serving life for the rape of Ms Burdett and attacks on 24 other women.
Mr Pora's lawyer, Jonathan Krebs, said they were pleased by the decision. He had earlier said compensation could be looked if there was no retrial.
There was no immediate comment from Solicitor-General Mike Heron or the police.
Ms Burdett's brother, Jim Burdett, said he was pleased Mr Pora would not be retried. He said he had come to the conclusion some time ago that he was not involved.
He had an open mind about whether Rewa should be tried a third time for his sister's murder but did want justice for her.
"With the quashing of the convictions, in principle it is the same situation [as in 1992], it means the murderer is still out there."
Fight for freedom
1992, March 23: Susan Burdett raped and murdered in her home in south Auckland.
1993, March 23: Teina Pora charged with burglary, sexual violation and murder.
1994, June: Pora convicted as a party to the rape and murder on the basis of confessions he made. Sentenced to life in prison.
1996, May: Rewa arrested after attacking a young woman in the inner Auckland suburb of Remuera, DNA from Rewa's father found to match semen from Burdett crimescene.
1998: Rewa eventually convicted of the rape of 27 women, including Ms Burdett but two juries fail to reach a verdict on murder.
1998, May 30: In 1998 Rewa was convicted on multiple sex charges dating back to 1987 and sentenced to preventive detention with a minimum non-parole period of 22 years. He was convicted of the rape of Ms Burdett the following year.
1999: Court of Appeal quashed Pora's convictions as a result of the DNA evidence implicating Rewa and evidence that Rewa acted alone.
2000, June: Pora was again convicted at his retrial, based on his confessions and witnesses, some of whom it later emerged were paid. His appeal to the Court of Appeal was dismissed.
2009, September: Private investigator and former police detective Tim McKinnel visits Pora in prison and is given permission to make inquires on Pora's behalf.
2011, September: Pora team file notice of application for the Royal Prerogative of Mercy but two years later are granted an appeal to the Privy Council.
2012, May: Police's criminal profiling expert goes public in Herald with view Pora not involved; Pora's team sue police claiming it is unlawfully withholding evidence, Ms Burdett's brother says Pora is innocent.
2013, February: It is revealed police paid some prosecution witnesses.
2013, August: The Police Association call for an independent inquiry into Pora's convictions.
2014, April: Pora granted parole at his 13th appearance before the board and after spending 21 years in jail.
2014, November: Five-member Privy Council panel hears appeal.
2015, March 3: Privy Council quash convictions.
