Judge Jane Farish ruled that extradition would not be "unjust or oppressive'' to McGrath.
McGrath was in court today and represented by lawyer Phillip Allan to hear the news.
He seemed confused by the ruling, but did not outwardly express any emotion.
The judge remanded him on bail under existing conditions. McGrath will stay at a Christchurch address until June 26 when he will have to turn himself in to Christchurch Men's Prison.
He could also voluntarily travel back to Australia before then if he wishes, the judge said.
Legal aid and representation will be available to him in Australia, Judge Farish told him.
She also made sweeping suppression orders, after requests by The Commonwealth of Australia, to "ensure the integrity of trial'' and to mirror existing suppression orders in place in Australia.