Andrew Soper, 74, fled to Kosovo with £182,000 from the Vatican bank in a bid to avoid prosecution for molesting boys at fee-paying St Benedict's School in Ealing, west London.
The former Ealing Abbot, known as Father Laurence, was extradited to face 19 charges of indecent assault and buggery against 10 former pupils in the 1970s and 80s.
A jury at the Old Bailey deliberated for 14 hours to find him guilty of all charges by a majority of 10 to two.
There were gasps in the public gallery as the verdicts were delivered while Soper stood in the dock impassively.
Judge Anthony Bate remanded Soper in custody to be sentenced on Tuesday December 19.
The scandal-hit school counts former Conservative chairman Lord Patten and entertainer Julian Clary among its old boys and currently charges fees of around £5,000 a term.
It had come under scrutiny in the past, with both violence and sexual abuse by the adults in charge said to be "prevalent".
Prosecutor Gillian Etherton QC told how the victims were subjected to sadistic beatings by Soper 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.
She added: "It is the prosecution case that 'punishments' as described by the complainants in this case were carried out by Soper in entirely inappropriate ways and circumstances and on many occasions with what can only have been sexual motive."
Ms Etherton said at least one of Soper's alleged victims subsequently suffered serious mental health problems, while another was too afraid to speak out because the abusers "were like saints to me".
Jurors heard how the first complainant suffered from "flashbacks" and "nightmares" about his treatment at Soper's hands.
He said he did not come forward sooner because he felt "too embarrassed" and feared being beaten or not believed.
The court heard Soper quit as an abbot in 2000 and moved to Rome then skipped bail and spent six years living in Kosovo, with a European Arrest Warrant issued for his extradition.
Giving evidence, Soper 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.
He told jurors he went on the run out of "stupidity and cowardice", fearing that his life's work would be wrecked.
He said: "If you want to destroy a priest, vicar, anybody, all you have to do is make an accusation up against them. Their future is ruined, their character is ruined."
Soper was on first name terms with Cardinal (Basil) Hume and knew Lord Patten, who worked on the advisory panel while he was Abbot, the court heard.
He is the latest in a string of men to face allegations relating to their work at St Benedict's.
In 2009, Father David Pearce, 75, nicknamed the "devil in a dog collar", was jailed after he admitted 11 charges of indecent assault dating back to 1975.
Between 2003 and 2009, "master of discipline" John Maestri, 78, of Chatham in Kent, admitted five indecent assaults against children at St Benedict's in the 1970s and 80s and was jailed.
In 2010, John Skelton was convicted of indecent assaults against two complainants said to have occurred in 1983 at St Benedict's.
Father Anthony Gee faced accusations of abuse, but no further action was taken although civil action was brought against him, jurors were told.
In 2010, Abbot Shipperlee announced an independent review of safeguarding arrangements, policies and procedures.
The following year, Lord Carlile produced a damning report calling for tougher rules to protect all faith pupils and stripped monks of control at the school.
He blamed the abusers for their "abject failure of personal responsibility and self-control", but also accused the monastic community for its "lengthy and culpable failure to deal with what at times must have been evident behaviour placing children at risk".
Pearce's crimes illustrated how "St Benedict's rule of love and forgiveness appears to have overshadowed responsibility for children's welfare", he said.
London CPS lawyer Tetteh Turkson said: "Soper abused his position as a teacher and as a priest to abuse children for his own sexual gratification.
"He compounded this by trying to evade justice and fleeing to Kosovo in order to go into hiding.
"The victims' bravery in now coming forward and giving evidence has seen him convicted of these serious offences."
In a statement issued by Lord Carlile QC, the school apologised unreservedly for the "serious wrongs of the past".
He said: "My client St Benedict's School is deeply concerned for and distressed by the ordeals faced by the victims of Laurence Soper, who have lived with the pain of his activities for so long.
"The school regrets that Soper did not have the courage to plead guilty. The result has been that innocent victims, whom he abused when they were boys in the school, were compelled to give evidence.
"The fact that these matters took place many years ago does not mitigate the pain and injustice endured by them."
He added: "The tough lessons of the past have been learned, and the errors and crimes of the past are in the daily consciousness and conscience of the school management.
"Child safeguarding is the top priority, alongside the highest level of teaching and the provision of an excellent learning experience."
Detective Superintendent Ang Scott, of Scotland Yard, said: "Soper was a manipulative individual who abused his position of trust as a headmaster of a middle school, who was responsible for discipline.
"Whilst preparing the boys for a caning, which is now illegal in schools, Soper asked them to remove clothes and he would then sexually assault them.
"This was a gross breach of his position, which has resulted in psychological trauma caused to a number of former pupils of St Benedict's.
"I would like to pay tribute to the victims in this case for the bravery they have showed in coming forward and reporting these offences and giving evidence in court."
An NSPCC spokesman said: "Instead of protecting the children in his care, Soper abused his position of trust at the school and subjected his victims to sustained, sickening abuse.
"The impact of that suffering will have had consequences not only during childhood but also into their adult lives.
"This case highlights once again that victims of past abuse can come forward and achieve justice no matter how long ago the offences took place and no matter who their abuser is."