The decision means Philip Wilson, who resigned as archbishop of Adelaide after his conviction, will avoid jail, the BBC reported.
Wilson, 67, is the world's most senior Catholic cleric to be convicted of covering up sexual abuse. His lawyers said they would lodge an appeal on Tuesday.
A magistrate said Wilson would commence his sentence immediately at a relative's home, where he would be monitored by a tracking device. He will be eligible for parole after six months.
As he left court on Tuesday, Wilson did not respond to an abuse survivor who confronted him to demand an apology, the BBC reported.
During his trial, Wilson denied knowing that paedophile priest James Patrick Fletcher had abused altar boys in the 1970s.
However, the court ruled in May that Wilson had been alerted to the abuse by victims, and failed to report it.
Fletcher was convicted of nine child sexual abuse charges in 2004, and died in jail in 2006.
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