John Farrell, 73, and Paul Kelly, 64, were convicted of several charges against six former pupils of St Ninian's School in Falkland, Fife, after a long-running trial at the High Court in Glasgow.
The school was run by the Catholic religious order the Congregation of Christian Brothers and housed around 45 vulnerable boys in need of care until its closure in 1983.
The men were remanded in custody after a jury found Farrell, from Motherwell, North Lanarkshire, guilty of three counts of indecent assault and a charge of assaulting a boy with a belt.
Kelly, from Plymouth, Devon, was convicted of four counts of indecent assault and three assault charges, including hitting a boy's head off sinks at the school.
The court heard they committed the crimes over a four-year period from 1979 against pupils aged 11 to 15.
After eight days of deliberations on more than 50 charges they were found not guilty of all but 11.
Their victims were in court for the verdict and cried out "yes" when the judge told the men they would be remanded in custody.
Police Scotland said Kelly and Farrell - headmaster of St Ninian's at the time of the offences - had betrayed pupils' trust "in a despicable manner".
Chief Inspector Nicola Shepherd, who led the investigation, said: "For a number of years, these men, who were placed in a position of trust, carried out prolonged abuse on a significant number of vulnerable young people.
"They betrayed that trust in the most despicable manner possible and subjected their victims to years of suffering.