The man, who had a vasectomy in 1994, met the woman who would become his wife in an internet chat room in 2000. The woman, who had an 18-month-old son, was living in the US.
The man admits he agreed to be falsely recorded as the father on the boy's birth certificate to meet US immigration requirements, allowing the child to settle in Australia. He and the boy's mother signed an affidavit of parentage in the US in which the man waived his right to blood or DNA tests.
But the man, who divorced the boy's mother in 2006 after four years of marriage, now says he does not want any relationship with the boy. And he believes that he should not be financially responsible for the 10-year-old.
Three Family Court appeal judges dismissed an appeal by the man's former wife and reinstated an original judgment that ordered the man to take a DNA test.
The boy's mother had sought a court order requiring contact between her son and former husband once a fortnight. She also sought an order that he ''maintain a residence'' for her and her son.
In 2007 a magistrate made an interim order that the former husband pay $800 a fortnight spousal maintenance.
At the time of the appeal, the Child Support Agency was collecting the money but not handing it over pending the outcome and parental testing.
The boy's mother told the court the dispute had caused her son ''severe psychological damage''.
In her appeal, she unsuccessfully argued that the trial judge should have applied US rather than Australian law. She claimed the judge had denied her procedural fairness.
The appeal judges agreed only that the primary judge had failed to consider the child's best interests. They dismissed the appeal, saying Australian courts had for decades recognised a child's interest in finding his true parents.
The judges said: ''This recognition by the law of the child's long-term interest in knowing the truth about his parentage, coupled with the likelihood … of the child already being aware - or of his becoming aware in the future - of the controversy surrounding his paternity, must outweigh not only the wife's expressed concerns regarding the threat to his loss of identity but also the emotional and psychological harm which she reports he has suffered.''
They said concerns raised by the wife were serious, bearing in mind that if the DNA test shows the man is not the father, this will be the only certainty the child will have. ''He will not know who his true father is.''