Update - 3.40pm: The Taoiseach has addressed the Dáil and has made a formal State apology for the "the humiliation, the disrespect and the deceit" to the women and families impacted by the CervicalCheck controversy.
Mr Varadkar said: "What happened to so many women and families should not have happened.
"It was a failure of our health service, State, its agencies, systems and culture.
"On behalf of the Government and the State, I am sorry it happened. And I apologise to all those hurt or wronged."
Vicky Phelan, Lorraine Walsh, Stephen Teap and others from the 221+ group were present in the public gallery as Mr Varadkar apologised for the "litany of failures" in how cervical screening in Ireland was operated.
Earlier: The Taoiseach is expected to say the State should have informed women they were given incorrect all-clear results and will accept the findings of independent reports into the issue.
More than 1,000 women and their families have been affected by the crisis which came to light in April last year after campaigner and one of the women affected Vicky Phelan went public.
Dr Gabriel Scally, the public health doctor who investigated the CervicalCheck controversy said it was fitting that the State now apologises to the women.
He said the apology from Mr Varadkar was a "momentous and unprecedented" step.
He said women and their families affected by the scandal wanted three things: to be told what went wrong and why, an apology and steps are being taken to ensure it doesn't happen again.
Today at 3pm An Taoiseach @LeoVaradkar will give a Formal Acknowledgment and Apology to all the Women and Families affected by the CervicalCheck Debacle in Dail Eireann. A statement from 221+ will issue afterwards. Watch live at Oireachtas TV at 3pm - https://t.co/6cNqQcacg0— 221+ (@221plus) October 22, 2019
He said the final piece was being addressed today when the State formally apologies to the women.
Professor of Health Systems at the School of Nursing in DCU, Anthony Staines says he is not sure if the apology will change the culture in the HSE.
"I do notice the National Screening Service has in the last day or two advertised for a new chief executive and I am hoping that they will get somebody really, really good," said Prof Staines.
"The staff in this organisation are not perfect but this organisation could be made sing with the right management."
Labour's health spokesperson, Alan Kelly, says the apology is overdue.
"I absolutely believe that this is a momentous occasion for the women and their families because this apology should have come some time ago," said Deputy Kelly.
"The women who were affected by this scandal deserve this and I am very happy that it is happening today."
Almost 80 members of the 221+ group will attend today's event with family members roughly doubling the number.
They say they hope the Taoiseach's apology brings some healing to those impact.
They also hope it marks a turning point in the State's provision of essential health and support services for women in Ireland.