Andrew Soper, 74, fled to Kosovo in 2011 to avoid prosecution over charges he molested boys at St Benedict's School in London.
He was extradited in 2016 to face 19 counts of indecent assault and buggery against 10 former pupils in the 1970s and 1980s.
A jury in London found him guilty of all charges. Soper, who faces about 10 years behind bars, is to be sentenced on December 19.
Prosecutor Gillian Etherton told the court how Soper's victims were subjected to sadistic beatings for "fake reasons".
They included kicking a football "in the wrong direction", "failing to use double margins", and "using the (wrong) staircase", leading to a caning and a sexual assault, she said.
On many occasons, there "can only have been sexual motive" for the punishments, she said.
Giving evidence, Soper, formerly known as Father Laurence, denied using the cane as a ruse to abuse boys who were given the choice of six lashes with trousers on, or three with them off.
The court heard he was on first name terms with Cardinal Basil Hume and knew former Hong Kong governor Chris Patten, an ex-pupil who served on the advisory panel when Soper was the abbot.
Previously, three people at the fee-paying school have been convicted of indecent assault.
The school apologised "unreservedly" and said it was now a "completely different institution".
"Soper abused his position as a teacher and as a priest to abuse children for his own sexual gratification," said Tetteh Turkson from the state Crown Prosecution Service, following his conviction.
"He compounded this by trying to evade justice and fleeing to Kosovo in order to go into hiding."
Police Detective Superintendent Ang Scott said Soper was a "manipulative individual" who abused his position of trust.
Whilst preparing the boys for a caning, Soper "asked them to remove clothes and he would then sexually assault them".
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