Henry Moloney worked at the time as a choirmaster and music teacher at Rockwell College, near Cashel, County Tipperary.
The 77-year-old, of Kimmage Manor, Dublin, was found guilty of seven counts of indecent assault on the schoolboy.
He had denied the charges.
The victim had told Clonmel Circuit Court how the abuse began near the start of a school year after Moloney asked him to join the choir.
He said although he knew what had happened was wrong, he thought no-one would believe him instead of a priest.
The offences all took place in the course of one school year, in the college's chapel and in Moloney's room there.
Moloney is due to be sentenced on 15 December.
A former priest has been found guilty of indecently assaulting a secondary school student in the 1980s in the Republic of Ireland.