Police said most of the passengers were from the Middle East and did not hold visas allowing them into the country.
They allege Radhi negotiated the passengers' fares, controlled their movements while they were in Indonesia and helped them to board the SIEV X.
Radhi was granted refugee status and has been living in New Zealand since 2009.
An arrest warrant was issued for him in the Brisbane Magistrates Court in February 2011, alleging attempted people-smuggling and, in July that year, Radhi was arrested in his Auckland home.
In order to be extradited, the Crown needed to show that Radhi had broken a comparable offence in New Zealand and the penalty had to be longer than a year in prison.
Judge Jonathan Moses in the District Court granted his extradition to Australia last March, which Radhi appealed in the High Court.
His lawyer Roger Chambers argued the boat had never made it near to Australian waters before it sank and no illegal immigrants had arrived in Australia.
He also pointed out that Radhi had not committed any alleged offences in Australia so was not bound by the New Zealand-Australia extradition agreement.
Crown lawyer Christine Gordon QC said Radhi had been accused of committing an extradition offence and New Zealand courts had jurisdiction.
In his decision released today, Justice Edwin Wylie said that at the time of the alleged offending, the maximum prison term was three months.
"Mr Radhi is therefore not eligible for surrender in relation to the offence for which extradition is sought."
Two other men, Abu Quassey and Khaleed Daoed, are in prison for their role in organising the SIEV X voyage.
Quassey was sentenced to seven years in an Egyptian jail and Daoed is serving a sentence of nine years in a Queensland prison after he was convicted of people-smuggling in 2005.
