Former monk Denis Alexander, 85, preyed on the children while teaching history at Fort Augustus Abbey school in the 1970s. Alexander targeted the boys during yoga classes and at his study in the institution.
A judge told him at the High Court in Edinburgh: "You have brought lasting shame on the Order of which you were a member."
The judge acknowledged that he had no criminal record prior to or since the offending and was now in poor health.
He told him he would have faced a five and a half year prison term but for his guilty pleas. The judge told the Australian citizen that he would be subject to deportation.
Alexander later left Scotland and became a priest in Sydney, in Australia, where he initially contested a bid to extradite over his crimes.
Efforts to bring him to justice after a BBC documentary called Sins of Our Fathers was shown in 2013. His victims found the courage to contact the police.
Alexander was returned to Scotland almost three years after an extradition request was first sent to the Australian authorities.
He admitted two charges of indecent behaviour against the boys at the High Court in Edinburgh last month after being brought into the building in a wheelchair.
Advocate depute Jane Farquharson QC told the court: "These offences committed by this accused Denis Alexander are a snapshot of what is believed to be wider systemic abuse of children within the Fort Augustus Abbey School and its preparatory school Carlekemp, also run by the Benedictine Order."
The prosecutor said the school was a subject of the Scottish Child Abuse Inquiry during 2019 and the English Benedictine Congregation accepted physical and sexual abuse of children took place. A sincere apology was tendered.
Alexander was known as Father Chrysotum when he taught at the Highland institution, where he also tutored pupils in bagpipe playing.
Alexander left the school during the 1970s and stopped being a practising Benedictine monk, but remained a priest and moved to Australia.
Ms Farquharson said: "He came to the attention of the police as a result of a BBC documentary screened in the summer of 2013 called Sins of Our Fathers that focused on life within both institutions."
The Crown Office requested his extradition in August 2016 and a warrant was issued by an Australian court in January the following year. But Alexander did not consent to his return to Scotland to face justice.
After further legal proceedings he did not continue to fight the move and came back to the UK in January 2020. Ms Farquharson said: "Significant delays were occasioned in bringing the accused to Scotland as a result of his opposition to the extradition process."
Defence solicitor advocate Shahid Latif said: "He is sorry and he can do no more than he has done and that is to have plead guilty."
He said that Alexander had been in "a stressful working environment" at the time of the offending and worked long hours seven days a week.
Alexander watched today's sentencing proceedings via a video link to prison. He was placed on the sex offenders' register indefinitely.