The Vatican appointed Bishop Gregory O'Kelly as a caretaker over the archdiocese, but has not moved to permanently replace Wilson.
Another victim, who can not be named, testified that Wilson had told him he was telling lies, and to recite 10 Hail Mary prayers as punishment.
Catholic Archbishop Philip Wilson has been sentenced to 12 months' detention.
Wilson has not resigned as archbishop, despite relinquishing his duties in the wake of his conviction.
'I do feel I've got justice, ' Feenan said after the sentencing. "However if I am unsuccessful in my appeal, I will immediately offer my resignation to the Holy See".
The case is a triumph for prosecutors who were able to convince the court, despite the passage of time, that between 2004 and 2006 (when the priest was in jail facing charges) Wilson remembered the incident 30 years before and believed the boy's allegations were true but still failed to report them.
The archbishop is likely to serve his sentence under house arrest and be fitted with an electronic monitoring bracelet, according to media reports.
Outside the court, abuse survivor Peter Gogarty said the fact Wilson has been convicted was "significant", but the sentencing not being custodial was "disappointing". Wilson would begin his climb through the church's hierarchy, which would culminate in him becoming the Archbishop of Adelaide in 2001.
Newcastle Local Court magistrate Robert Stone found him guilty of concealing a serious indictable offence of another person, concluding his primary motive was to protect the church.
Archbishop Wilson was released on bail until a final hearing in August after he is assessed for whether he can serve the 12-month jail sentence as home detention.
Wilson will be eligible for parole after six months, emailed court documents show.
The magistrate found Wilson had at that stage obtained the level of belief needed to report what he knew to authorities.
The maximum penalty for concealing child sex abuse is two years behind bars.
With Wilson's age and health, a jail term would be detrimental to him, his lawyers argued.
It is not known whether he will appeal the sentence.
It's expected he'll serve the term at home. One, Peter Gogarty, said it was "probably letting (Wilson) off a little bit too lightly". "It's an absolutely strong message today".
Like elsewhere in the world, Australia has been plagued by accusations that the Catholic Church ignored and covered up child abuse.
He also called for Wilson to resign as archbishop.
"Those who hide abuse and shield perpetrators from accountability ... are demonstrating that you are placing the needs of the perpetrator as a higher priority over the needs of victims and their families", Mr Stone said.
"It is a source of great grief and shock to the Catholic community here that he has been found guilty of concealing the appalling crimes of another priest, the convicted paedophile James Fletcher, now deceased", Bishop Wright said.