The New South Wales Director of Public Prosecutions will not appeal a decision to overturn the conviction of the former Catholic Archbishop of Adelaide Philip Wilson on charges of concealing historical child sex abuse in the Hunter Valley.

Archbishop Wilson was the highest-ranking Catholic in the world to be convicted of concealing abuse until his conviction was overturned by the Newcastle District Court earlier this month.

"The Director of Public Prosecutions has no right of appeal against the dismissal of a charge in these circumstances," it said in a statement.

"An appeal can only be made on errors of law.

"After careful consideration, it was decided that there were no reasonable prospects of success of appeal on errors of law."

The Apostolic Administrator of the Catholic Archdiocese of Adelaide, Bishop Greg O'Kelly, said he was "delighted at the news".

"We are very satisfied with the outcome and await the appointment of a new Archbishop of Adelaide," he said.

"Emeritus Archbishop Wilson, who resigned on July 30, will now have the opportunity to recuperate and gain strength after this ordeal."

The charges related to an allegation that in 1976, 15-year-old altar boy Peter Creigh went to Father Philip Wilson on two occasions and told him that four years earlier he had been abused by a fellow priest, James Fletcher.

During court proceedings, Archbishop Wilson's legal team acknowledged that Mr Creigh had been abused, but continually denied that the clergyman knew of that abuse at the time.

Newcastle Local Court convicted Father Wilson in May of concealing the abuse and he had been serving a minimum sentence of six months in home detention before the conviction was overturned.

Peter Creigh told the ABC it had been a long fight.

"We always knew it was going to be a very difficult case to prove, it is one that had not been tested before, but we should be very proud of what we have been able to achieve and what we have highlighted," Mr Creigh said.

"It was like a tennis match, we won the first set, they won the second and there was no third set."

NSW Detective Police Inspector Jeff Little headed the strike force set up to investigate the matter.

He said he would continue to support all those involved.

"Certainly Mr Creigh has been involved in this matter for five years and it has been a long and arduous journey for him and, as I say, for a whole lot of other victims as well," he said.