Claims of abuse are being made by 170 former pupils of St William's in Market Weighton, East Yorkshire.
Judges said the De La Salle Brotherhood was liable along with the Middlesbrough diocese which owned the school.
St William's, which looked after boys aged 10 to 16 with emotional and behavioural problems until it closed in 1992, had been owned by the Roman Catholic Diocese of Middlesbrough, but many of the staff were members of the De La Salle Brotherhood.
A former principal at the school and former De La Salle member, James Carragher, was jailed in 2004 for abusing pupils.
"Civil claims for compensation for historical sexual abuse can be brought against organisations in two ways.
Organisations are automatically liable for the acts of people they employ. It's known as vicarious liability. They can also be sued in negligence if they failed to act to prevent sexual abuse when they had enough knowledge to know that it was a real threat.
However, negligence is not automatic. It has to be proved and that can be a complex process involving proof of complaints, the knowledge the organisation had of the issue, and whether any measures it put in place to prevent abuse were sufficient.
Claims in vicarious liability are therefore quicker and easier, and so the preferred route for claimants.
Today's judgement is of real significance because it broadens the traditional vicarious liability of organisations.
In the past this has largely been confined to the employer/employee relationship.
Today's ruling makes it clear that that can be an artificial distinction, and that liability can arise from other relationships which are akin to employment. That could have a bearing on claims arising out of the Jimmy Savile scandal."
Organisations are automatically liable for the acts of people they employ. It's known as vicarious liability. They can also be sued in negligence if they failed to act to prevent sexual abuse when they had enough knowledge to know that it was a real threat.
However, negligence is not automatic. It has to be proved and that can be a complex process involving proof of complaints, the knowledge the organisation had of the issue, and whether any measures it put in place to prevent abuse were sufficient.
Claims in vicarious liability are therefore quicker and easier, and so the preferred route for claimants.
Today's judgement is of real significance because it broadens the traditional vicarious liability of organisations.
In the past this has largely been confined to the employer/employee relationship.
Today's ruling makes it clear that that can be an artificial distinction, and that liability can arise from other relationships which are akin to employment. That could have a bearing on claims arising out of the Jimmy Savile scandal."
Mr Baverstock, from Bridlington, said he felt it was time for both the diocese and brotherhood to make settlement offers to stop the "protracted suffering" of the claimants, but feared the process of claiming compensation would be drawn out.
"They'll continue this game until all of us are dead, simple as that. We are all getting old, we have to live daily with the nightmares, with the knowledge of what went on."
The Court of Appeal ruled in 2010 that the Middlesbrough diocese was solely responsible for an £8m compensation claim.
In a statement, the diocese said it appealed against the 2010 ruling because "there was an important principle of justice at stake, that those who ran St William's on a day-to-day basis at the time the alleged abuse took place should share the burden of compensating its victims".
"We are also pleased that, now that the question of who is legally liable for the historic abuse at St William's has been decided, the individual claims for compensation can begin to be examined by the courts."
Humberside Police began an investigation in 2001, which focused on child abuse at the home.
Former principal Carragher was jailed for 14 years in 2004 for abusing boys in his care over a 20-year period.
Compensation claims on behalf of former pupils were first submitted in 2004. The alleged abuse is said to have taken place between 1958 and 1992.
Solicitor David Greenwood, who is representing the claimants, said: "This case should have been settled years ago.
