The out-of-court settlement far exceeds previous compensation awards made by the Catholic Church or religious orders in Australia in sex abuse cases.
A statement from the St John of God Brothers said: "The order acknowledges that some of the residents under its care were sexually abused by some brothers."
The disabled men, who were only teenagers at the time, were abused by up to 20 brothers in three Melbourne institutions run by the order over the past 30 years, a spokesman for the order said.
Many of the brothers are now dead. Several had been asked to leave the order or had left voluntarily, Reuters news agency quoted him as saying.
'Breach of trust'
St John of God has settled some previous claims alleging sexual abuse, but the amounts paid were much smaller.
The victims' lawyer, Peter Gordon, said individual compensation payments ranged from A$50,000 to A$400,000.
"Clearly the damage these people have suffered is significant and represents a breach of trust," he said.
Australia's Catholic Church has recently admitted that secrecy clauses were included in compensation payments to sexual abuse victims.
But John McCarthy, a lawyer for the Church, said Australia's bishops appeared to be unaware of the clauses, which effectively rendered any compensation as "hush money".
Archbishop's warning
The Church has confirmed that since 1996 it has paid A$3m in compensation to 101 sexual abuse victims in Victoria state alone.
Adelaide's Catholic Archbishop Philip Wilson will address the US Conference of Catholic Bishops called to discuss the child sex abuse scandal rocking the American Church.
The conference opens in Dallas, Texas, on Thursday.
In April, Archbishop Wilson described the scandal as a "firestorm" which could inflict "perhaps the greatest ever destruction of the Church in western civilisation".