Moko Sayviah Rangitoheriri, 3, died in August last year of horrific injuries inflicted by his carers.
In sentencing Moko's killers, Tania Shailer and David Haerewa, Justice Sarah Katz ruled that their previous convictions were "not relevant".
But she agreed to release the details to the Herald.
While Haerewa has a number of convictions for male assaults female, neither had been convicted of any charge relating to child abuse, neglect or maltreatment.
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When sentencing an offender, a judge must look at several factors including the seriousness of the crime, the impact on the victim and the offender's background and personal circumstances. The judge must also take into account any aggravating factors including the "number, seriousness, date, relevance, and nature of any previous convictions of the offender and of any convictions for which the offender is being sentenced or otherwise dealt with at the same time".
In the case of Shailer and Haerewa, Justice Katz decided that while between them their criminal history was extensive, none of their previous crimes was relevant to what happened to Moko.
Shailer's lawyer did not oppose the information being released to the Herald, but Haerewa's did.
The Crown also opposed publication of the couple's previous convictions on the basis that they were ruled "to not be relevant for sentencing purposes" and submitted that "the privacy of the defendants outweighs any countervailing interests in freedom of information".
However, Justice Katz decided:
"Given the strong public interest in this case and the broader issues it raises, I have concluded that principles of open justice, the freedom to seek, receive and impart information and the orderly and fair administration of justice outweigh any relevant privacy interests.
"The request for access to the defendants' criminal histories is accordingly granted."