The Magdalene Restorative Justice Scheme is to be expanded to include 14 adjoining institutions.
The Justice Minister Charlie Flanagan announced a "general" payment will be made for the entire period of residency and a "work" payment for the period of work in a laundry.
The Department of Justice said central guidance will also be drawn up on the development and operation of any future redress schemes.
The Minister said: “I am pleased to announce that the Government has agreed to my proposal to apply the Magdalen Restorative Justice Scheme to women who worked in the laundries and were resident in these adjoining institutions.
"This is an important step in implementing the key recommendation of the Ombudsman.”