Wilson, 68, became the world's most senior Catholic cleric to be convicted of covering up sexual abuse when his trial ended in May. A police investigation earlier this year found Wilson guilty of covering up sexual abuse of two altar boys by priest James Fletcher in the 1970s.
Fletcher was convicted of the abuse in 2004 and died in prison two years later.
At the earlier trial, Magistrate Robert Stone said Wilson had stayed silent about the abuse out of a desire to protect the Church's reputation. He then avoided jail after his conviction and was serving home detention.
Wilson later launched an appeal during which Newcastle District Court judge Roy Ellis was asked to consider whether prosecutors had proved beyond reasonable doubt that Wilson had failed to report allegations against Fletcher after the priest had been charged.
Ellis upheld Wilson's appeal on Thursday and quashed the sentence given by a lower court, the report said.
"There is no proper basis on which I can rely to reject the evidence of (Father Wilson)," Ellis said, according to national broadcaster ABC.
Wilson had said during the trial that he did not remember the victims complaining to him about the abuse.
The prosecutors, who had also filed a petition for Wilson to be transferred to a prison, did not comment whether they would challenge the verdict.
Australia's Royal Commission into Institutional Responses to Child Sexual Abuse reported that the Catholic Church received complaints from 4,500 people for alleged abuses committed by some 1,880 priests between 1980 and 2015.
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