David Edwin Rapson, 69, was working at Hobart's Dominic College in the 1980s when he used alcohol and cigarettes to befriend the three students, aged either 14 or 15.
He abused them on three separate occasions at a college dormitory, in a house during an altar boy trip, as well as in his office.
Rapson earlier pleaded guilty to three counts of indecent assault after being extradited to Tasmania from Victoria in May to face the charges.
He was already serving 12 years and six months' jail, with a non-parole period of nine years and four months, after being found guilty in 2015 of sexually abusing several boys at Victorian boarding schools in the 1970s and '80s.
In sentencing remarks published on Tuesday, Supreme Court of Tasmania Justice David Porter described Rapson's abuse of the three boys as a grave breach of trust.
"In two cases, the offence was in the context of mild or heavy intoxication of the victim from alcohol supplied," Justice Porter said.
"In the third case, the defendant took direct advantage of the victim's emotional state."
Justice Porter said if he was sentencing for each crime independently, Rapson would have received 18 months' jail on each count of indecent assault.
"However, the law requires me to take into account, among the other things I have mentioned, the lengthy sentence which you are presently serving," he said.
"I take the view that an additional minimum time in prison to that which you are presently subject is necessary."
Rapson was given a total sentence of three years' jail backdated to March, when he became eligible for parole from his Victorian sentence, with a non-parole period of 18 months.
Justice Porter said he was satisfied there were "very strong" signs of Rapson's rehabilitation.
He noted Rapson had an abusive childhood at the hands of his physically violent stepfather and two other men.
Justice Porter said Rapson had undergone therapy and described it as "very beneficial, allowing him to understand his offending and provide him with the skills to avoid further aberrant behaviour".
Justice Porter said he had to take into account the fact the offending was within the period covered by the Victorian sentence and the significant length of the 2015 non-parole period.
One survivor told the court Rapson's abuse had destroyed his faith in the Catholic church and pushed him toward self-destructive behaviours.
Another survivor said he tried to take his own life after being "consumed" by an article about Rapson's abuse in Victoria and feeling guilty for not doing anything about it.
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National Sexual Abuse and Redress Support Service 1800 211 028
