The abuse happened at institutions run by religious orders
The Irish Sisters of Mercy is to supply a 128m euros (£116m) package as reparation for decades of child abuse in its schools and orphanages.
In May, the Ryan report laid out a picture of systematic abuse.
The order of nuns ran five schools named in the damning report, including the notorious Goldenbridge.
The order said it was "deeply saddened at the findings" of the report and "wholeheartedly regrets" the suffering experienced by children in their care.
"It is the sincere hope and desire of the congregation that this contribution will help towards the enhancement of the lives of former residents", it added.
Overall, the offer is the largest made so far by any of the 18 Catholic religious bodies whose institutions were severely criticised for systemically abusing children in their care.
- Cash of 20m euros will be transferred to a trust for former residents
- Properties valued at 107.5m euros to be transferred to the state (80.8m euros), a trust for former residents (11.6m) and to voluntary groups (15m euros)
- The order has already contributed 33m euros and has committed to pay 1.9m euros to counselling charity Faoiseamh over the next five years
After the outrage which greeted the Ryan report, the Irish government made clear that the orders would have to come up with more compensation.
No real names, of perpetrators, appeared in the report after the Christian Brothers took legal action in 2004 to keep the identities of all of its members, dead or alive, out of the report.
More than 2,000 people told the commission they had suffered physical and sexual abuse as children in the institutions, which included schools and orphanages.
It found that sexual abuse was "endemic" in boys' institutions, and church leaders knew what was going on.
The report, nine years in the making and covering a period of six decades, also found government inspectors failed to stop beatings, rapes and humiliation.
separate report published last month
exposed the church's cover-ups of child sex abuse by priests in the Dublin Archdiocese.