On Tuesday Mr Kenny described the workhouses as "the nation's shame" and said state accepted its direct involvement. The apology comes two weeks after a report revealed thousands of women forced into the workhouses were verbally and physically abused.
The Irish leader was put under pressure to apologise after survivors said his comments expressing sympathy for those who endured the conditions of the laundries did not go far enough.
"Therefore, I, as Taoiseach, on behalf of the State, the government and our citizens deeply regret and apologise unreservedly to all those women for the hurt that was done to them, and for any stigma they suffered, as a result of the time they spent in a Magdalene Laundry," Mr Kenny said.
Twenty women who were locked up in one of the laundries attended a parliamentary debate to witness firsthand the Taoiseach's apology.
They held hands and wept as Mr Kenny spoke, before joining members of the Dail in giving the Taoiseach a standing ovation.
This is a national shame, for which I again say, I am deeply sorry and offer my full and heartfelt apologies.
Representative group Magdalene Survivors Together was also hoping to hear details of a compensation scheme and Mr Kenny said payments will be made along with other supports, such as medical cards and psychological and counselling services.
Judge John Quirke, the president of the Law Reform Commission, has been appointed to undertake a three-month review and make recommendations on payments.
"The terms of reference for Judge Quirke will be published later today and I will also arrange for the representatives of the women to be fully briefed on this process," Mr Kenny said.
"When Judge Quirke has reported, the Government will establish a fund to assist the women, based on his recommendations."
Maureen Sullivan was sent to a Magdalene laundry after he father died when she was 12. She said Mr Kenny had given survivors their lives back.
"He didn't hold back on anything," Ms Sullivan said. "He really did us proud."
An 18-month inquiry found more than 2,000 women were sent by authorities to the laundries.
It also found five areas in which there was direct state involvement in the detention of women in the workhouses, which were run by nuns.
The state found 10,000 single mothers, women, and girls as young as 11 were put to work in detention, mostly in the industrial for-profit laundries for reasons including petty crime, disability and pregnancy outside marriage.
Now we can go on with our lives and we know that we've got an apology, and he's taken responsibility. It's just fantastic.
Each of the women inside were renamed, and their surname unused. They could leave the laundries if they moved to other state-run institutions, such as psychiatric hospitals, in the company of police, probation, court or prison officers.
Some of those in the laundries received welfare and payments for services and the institutions were routinely checked by inspectors - known as "the suits"- to ensure the conditions complied with rules for factories.
The last Magdalene laundry closed in 1996 in Dublin.
The Dáil is due to debate the full findings of the report later this month. Its inquiry was prompted by a report from the UN Committee Against Torture in June 2011.
But those who were in state-run institutions in Northern Ireland say they are still waiting for their apology.
Margaret McGuckin described her time in a Magdalene laundry as a "nightmare" but said she and other children in the institution came to accept how they were treated.
"[I felt] they were holy nuns of God, that they were in the right, that this was the way things were done. We thought we were the lowest of the low and bad, bad people," she explained.
Margaret told UTV she believed no one would ever believe her if she told of her experiences, and she used alcohol to block out the memories of her childhood. Having lost faith in the hierarchy of the Catholic Church, Margaret has called for the perpetrators of the abuse to come before the courts.
"I want them to publicly apologise to us in the north also," she said.
If anybody has done any wrong or has covered up they do need to resign and their resignations need to be accepted.
"We are still left here, we are hoping for our justice for what's happened up here in the north. This needs to be taken into consideration. We are still waiting on an apology from the Executive, which I hope will happen very soon."
The McAleese report looked into Magdalene Laundries in the Republic of Ireland and Northern Ireland's historical institutional abuse inquiry, which began work in September last year, only covers abuse suffered by children in residential institutions.
Amnesty International said the treatment of adult women in these institutions has been overlooked.
Patrick Corrigan, Northern Ireland Programme Director of Amnesty International, has written to the Peter Robinson and Martin McGuinness asking them to address the issues of women abused in the state-run institutions.
"The First Minister and deputy First Minister responded with compassion and action when they heard the cry for justice of child abuse victims in Northern Ireland institutions. We hope that they will respond similarly to the calls from women who suffered as adults," he added.