Just announced by Minister for Justice, Equality and Law Reform. I am not sure what the reaction will be and if if goes far enough. Will update with more.

Update: The advocacy group Justice for Magdalenes have released a statement welcoming the inquiry but have expressed disappointment in the lack of an apology from the government.

          Statement on the Magdalene Laundries

The Government today considered the circumstances of the women and girls
who resided in the Magdalene Laundries.  The Government welcomed the
statement made last week by CORI on behalf of the four congregations, the
Sisters of Our Lady of Charity, the Religious Sisters of Charity, the
Sisters of Mercy and the Good Shepherd Sisters who indicated their
“willingness” to “bring clarity, understanding, healing and justice in the
interests of all the women involved”.  The Government believes it is
essential to fully establish the true facts and circumstances relating to
the Magdalene Laundries as a first step. The following has been agreed:

  1. An Inter-departmental Committee will be established, chaired by an
     independent person, to clarify any State interaction with the
     Magdalene Laundries and to produce a narrative detailing such
     interaction.

  2. The Minister for Justice, Equality and Defence, Alan Shatter TD and
     the Minister of State with responsibility for Disability, Equality,
     Mental Health and Older People, Kathleen Lynch TD are to meet with
     the religious congregations and the groups representing former
     residents of the Magdalene Laundries. Their discussions will include
     addressing the following matters;
        a. The making available by the congregations of all records
           maintained by them with regard to the residents of the
           Magdalene Laundries to enable all available information about
           former residents to be shared with them and also made available
           for appropriate research purposes.
        b. The provision of information concerning the number of persons
           currently residing with or in the care of the religious
           congregations who originally commenced such residence in the
           Magdalene Laundries  and who have remained in their care.
        c. To discuss the putting in place of a restorative and
           reconciliation process and the structure that might be utilised
           to facilitate such process.

The Minister for Justice, Equality and Defence together with the Minister
of State for Disability, Equality, Mental Health and Older People, will now
be following up on this Government decision with the relevant parties.
Consideration is being given to the appropriate independent person to
appoint to chair the Inter-departmental Committee. It was agreed by
government that an initial report should be made to Cabinet on the progress
being made by the Inter-departmental Committee within 3 months of its
establishment.