After a number of delays, the first payments are expected to be made in the second quarter of the year.
It comes after Taoiseach Leo Varadkar's apology following the publication of the final report of the Commission of Investigation into Mother-and-Baby Homes over three years ago.
Minister for Children Roderic O'Gorman said the redress scheme was a key element of the Government’s action plan for survivors and former residents of Mother-and-Baby homes and county home institutions.
He said his department has advised people that in the majority of cases, the process involves a simple application form and there will not be a requirement to submit records.
The payments range from €5,000 for mothers who were in one of the institutions for less than three months with those who spent up to six months entitled to €10,000 for example.
The figure increases with length of stay but there are very few women at the higher end of the scale.
However, 24,000 survivors were deemed ineligible to receive payment.
University of Galway lecturer and co-director of the Clann Project Dr Maeve O'Rourke described the situation as "unconstitutional discrimination".
"One of the huge problems with this scheme is that 24,000 of the estimated 38,000 people alive now who were born in the institutions are fully excluded from the scheme," Dr O'Rourke said.
She said: "So that's about two-thirds of the people still alive who were born in the institutions are not eligible at all.
"And that's because the Government has put a requirement that you have to have been kept in one of the institutions for more than six months.
"So people who were separated from their mother before the age of six months are considered not to have suffered harm, deserving of redress.
"It seems to me to be unconstitutional discrimination. We haven't had any rational explanation as to why a person who was in an institution for just over six months before being unlawfully separated, versus a person who was there for five months, 29 days, you know why they're different."
She added: "And so certainly, we've actually advised people to seek legal advice. I don't actually think this scheme will survive constitutional litigation, but that isn't something that people should be forced to do.
"The amounts are quite limited. For example, a woman as a mother who was detained for up to three months will be entitled to €5,000.
"So really for the sake of these payments, it's extremely upsetting for these people, and highly unfortunate that the Government hasn't yet amended it."
Dr O'Rourke also wants to see all those eligible for payments to be given an enhanced medical card as well.
Under the redress scheme, as currently designed, those who were detained in institutions for less than six months do not qualify for this card.
Dr O'Rourke said the crucial aspect of the abuse was the unlawful and forced family separation and the lifelong consequences as a result, not the number of months spent in the institution.
She said the enhanced medical court is something that everybody should be accessing including those who suffered abuse when they were boarded out.
Minister O’Gorman has also announced the appointment of the former CEO of the Adoption Authority of Ireland Patricia Carey to the role of Special Advocate for Survivors following a recruitment campaign through the Public Appointments Service.
Patricia Carey’s remit includes Mother-and-Baby Institutions, County Homes, Magdalen Laundries, Industrial and Reformatory Schools, and related institutions, and those adopted, boarded out, or the subject of an illegal birth registration.