Wilson is the most senior clergyman in the world to be convicted of concealing child sex abuse.
Wilson, however, may not spend much time in prison as he has to serve a non-parole period of six months, and can be assessed for home detention after that.
Archbishop Philip Wilson arrives for sentencing at Newcastle Local Court in Newcastle, Tuesday, July 3, 2018.
Lawyers for Wilson, who maintained his innocence throughout the legal process, had argued that he did not know that Fletcher had abused a boy.
Wilson has not resigned as archbishop, despite relinquishing his duties in the wake of his conviction.More news: Uruguay’s Edinson Cavani doubtful for France match
Another of Fletcher's victims, Daniel Feenan, would have preferred to see Wilson leave the court in handcuffs but hailed the magistrate's decision to impose a 12-month sentence.
Archbishop Wilson also told the court that if he had been notified of the scandal, he would have offered pastoral care to the victims and their families and reported the event to his superiors.
The sentence comes as abuse survivor Peter Creigh has said he wants Wilson locked up to send a message to religious leaders that institutional cover-ups will no longer be tolerated.
Allegations of sexual abuse cover ups have continued to rock the Catholic Church years after perpetrators of sexual abuse started regularly appearing before the courts. Judicial sources did not clarify whether Wilson would enter prison.
If Pope Francis doesn't sack the archbishop, he becomes "part of a laughing stock", an advocate for abuse survivors says.
"It is a deep shock and disappointment that this man has been found guilty of covering up abuse", Wright said in a statement.More news: Reports of hidden N.Korea nuclear efforts raise questions in US
Stone found the 67-year-old cleric guilty in May in the Newcastle Local Court of failing to report to police the repeated abuse of two altar boys by pedophile priest James Fletcher in the Hunter Valley region north of Sydney during the 1970s. "So I am content that we've done something in Australia that nobody else has been able to manage".
Archbishop Philip Wilson was convicted in May.
"Survivors have been vital in helping us learn the lesson of our shameful history of abuse and concealment, which was laid bare in the Royal Commission into Institutional Responses to Child Sexual Abuse and state inquiries, including the NSW Special Commission of Inquiry" in Newcastle in 2013. Wilson was charged in 2015, accused of failing to report Fletcher's abuse to police.
On the day Wilson was convicted, Criegh, who waived his right to a non-publication order on his name, said it was a "very, very significant day".
Tens of thousands of children had been abused in various Australian institutions, including the Catholic Church over the last 90 years, the commission estimated.
Peter Gogarty, another victim of Fletcher, said Wilson's sentence could open the floodgates around the world and empower more victims to speak up.More news: Man Accused of Stabbing 9 People At Child's Birthday Party in Boise
In recent weeks, Pope Francis has said he felt ashamed of the church's failure to listen to victims of child sex abuse and has called for an end to the culture of abuse and coverup.