The Magdalene Restorative Justice Scheme is to be widened to include 14 adjoining institutions.
The Minister for Justice said these include all of the institutions recommended by the Ombudsman.
The scheme will apply to women who worked in the laundries and who were resident in the 14 institutions.
A "general" payment will be made for the entire period of residency and a "work" payment for the time spent in the laundry.
Minister Charlie Flanagan said: "I am pleased to announce that the Government has agreed to my proposal to apply the Magdalene Restorative Justice Scheme to women who worked in the laundries and were resident in these adjoining institutions."
He continued: "This is an important step in implementing the key recommendation of the Ombudsman."
In January, the Ombudsman Peter Tyndall criticised the exclusion of some of the women who had worked in the institutions but who were not included in the scheme.
The Magdalene Restorative Justice scheme was set up in 2013.
Since then 692 applicants have been paid just over €26 million in lump sum payments.
Barrister Maeve O'Rourke is the senior research and policy officer with the Irish Council for Civil Liberties who has worked with Justice for Magdalenes and brought their case to the UN committee against Torture.
She expressed relief that the women who had been fighting for inclusion in this scheme for so long have finally been admitted.
Ms O'Rourke said their exclusion was very unfair because the state had always accepted they worked as children in the laundries but they were registered by the nuns on the books of adjoining institutions which was the technical reason for their exclusion.
Regarding families of former residents who may be dead she said her understanding is that families can benefit from the scheme if women applied to it before they passed away.
She said this development rights a historical wrong.
She said the women were locked away and subjected to forced labour which were both violations of their human rights.