The Government is opening a three-month window for certain immigrants from outside the European Economic Area to apply for permission to remain in Ireland.
The decision follows concerns raised by the Supreme Court in two cases, and is intended to address the difficulties facing a significant number of so-called "undocumented" persons residing here.
To qualify for the new scheme, non-EEA nationals must have held a valid student permission from January 2005 to December 2010, but have not obtained an alternative immigration permission since then.
Between today and 20 January 2019, applicants can apply for the new scheme which provides a pathway for groups described by the Supreme Court as "settled migrants" - and for those who have become undocumented through losing their previous permission to remain in the State.
Successful applicants will not be entitled to bring family members to join them in Ireland under family reunification.
However, the Department of Justice said the family circumstances of persons present in the State will be taken into consideration - and the family unit who have been residing with them in the State may be given permission to remain under the scheme.
Successful applicants will be granted a "4S" stamp permitting them to live and work in Ireland for two years without an employment permit.
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Applicants must not engage in criminal activity, must reside continuously in the State, make every effort to gain employment and not be an undue burden on the State.
They must also acquire at least minimum English language skills by the end of the two-year period.
Minister for Justice and Equality Charlie Flanagan said that after a probationary period of two years, those deemed eligible will have to apply for renewal - but at this point they will have to prove that they are self-sufficient and will not become an "unreasonable" burden on the State.
He said that in such cases, the beneficiaries would be expected to become net contributors to the economy.
All applicants must pay €700 upfront when submitting their applications.
€250 is non-refundable, while €450 will be refunded if the application fails.
Successful applicants issued with an initial two-year permission will be charged a further €300 at that point - half the usual fee of €600.
The new scheme was prompted by the "Luximon" and "Balchand" cases, in which the Supreme Court ruled that when the Minister for Justice is considering applications for a change of status of "timed out" students or undocumented migrants, he must by law consider their private and family life rights.
The case was expected to have a huge impact for people arriving in Ireland on valid student visas but who subsequently became undocumented through no fault of their own.