He had also been accused of sexual abuse in the United States.
Bernard Hartman, who returned to Australia from the US in 2013 to face the charges, had been accused of abusing four children in the 1970s and 1980s, when he had been working as a teacher at secondary school, St Paul's College.
USA Today reported that he pleaded guilty in Victoria state County Court, to four counts of indecent assault against two girls, and pleaded not guilty to offenses against two male former students.
He was convicted of one count of indecent assault and two counts of common law assault against one of the men, and was found not guilty of another five counts of indecent assault against the same man.
In a separate trial last week, he was found not guilty of one charge of indecent assault against the second man.
Mr Hartman had moved back to the US in the 1980s to continue to work as a teacher, including at a Catholic high school in Pittsburgh.
In 2014 the head of a St. Louise religious order said sorry following allegations of abuse against Hartman and seven other brothers who worked at the Pittsburgh high school.
These cases were revealed after the Catholic Diocese of Pittsburgh learned about the charges against Hartman in Australia.
The diocese sent letters informing graduates and consequently received another allegation against Hartman who was last thought to have taught at the school in 1997.
More than 20 other allegations were made against seven other brothers.
Hartman will be sentenced in Australia at a later date.
