In 2012, a New Zealand District Court ruled Radhi to be extraditable.
However, that was overturned in the High Court because Radhi's charges were seen not to meet the threshold for extradition at the time of his alleged offending.
Police appealed against the decision at the Court of Appeal in Wellington and a decision released today ordered the case to return to the District Court.
It also ordered for a warrant to be issued to detain Radhi.
In order for Radhi to face extradition the alleged offence he committed in Australia would have also had to be an offence if he had committed it in New Zealand, the ruling said.
During the appeal, lawyer for the police Christine Gordon QC told the Court of Appeal that Radhi had "done everything in his power" to commit the offence, but factors outside of his control took over and the asylum-seekers did not make it to their destination.
The offence was that he aided the immigrants to attempt to illegally enter Australia, she said.
Radhi's lawyer Roger Chambers told the court the events were "tragic beyond measure".
But he said that for a crime to have been committed, the boat would have needed to reach New Zealand.
The vessel sank either in Indonesian waters, or it "may have edged" into international waters, but it was definitely not in Australia waters, he said.
However, in their ruling Justices Ellen France, John Wild and Douglas White disagreed that for an offence to be committed it would need to have happened in New Zealand.
"The offence is wilfully aiding or assisting another person so they can arrive in New Zealand.
"The physical element of the offence is the aiding or assisting, while the mental element is doing so 'wilfully'. Arrival is the aim of the aiding or assisting. The words 'to arrive' look forward to something that may - or may not - happen," they said.
