The Supreme Court has refused to hear a further appeal by a Dublin woman who wanted to challenge the result of the referendum repealing the Eighth Amendment.
The decision clears the way for the Government to bring in legislation to give effect to the result and amend the Constitution.
The Taoiseach said today's judgment means the referendum result can now be signed into law.
Legislation to allow for abortion in certain circumstances is now on track to be passed by the Oireachtas before Christmas, Leo Varadkar told the media on the final day of his party's think-in in Galway.
Mr Varadkar said the Government intended to have services in place "for Irish women who need them" in January.
The referendum on whether to change the Constitution to repeal the Eighth Amendment took place in May.
The Yes side received 66.4% of the vote with 33.6% voting No. Just one constituency, Donegal, rejected the proposal.
The country voted to repeal the Eighth Amendment by a majority of 706,349 votes.
The Eighth Amendment, which was inserted into the constitution in 1983, recognised the equal right to life of the mother and the unborn, and limited the circumstances whereby abortions could be carried out.
Joanna Jordan, of Upper Glenageary Road, Dún Laoghaire, Co Dublin was refused permission by the High Court to bring a petition challenging the result of last May's referendum.
Mr Justice Peter Kelly said she had not met the necessary legal test under the legislation before a court can permit such a petition to be brought.
She then appealed that decision to the Court of Appeal, which upheld the refusal.
It also found Ms Jordan's action amounted to a frustration of the democratic process in relation to referendums.
She had complained about statements made by Mr Varadkar and Minister for Health Simon Harris during the campaign and claimed there were irregularities in the conduct of the referendum and registration of voters.
She had sought to bring a further appeal to the Supreme Court but in a determination issued this afternoon, the court ruled that no such appeal will be permitted.
The determination was made by Chief Justice Frank Clarke, Mr Justice Donal O'Donnell and Mr Justice Peter Charleton.
The Supreme Court said that for leave to appeal to be given, the court had to be satisfied there were stateable grounds of appeal involving issues of principle.
It said the law in this area was already well settled as a result of previous decisions of the court.
It ruled there was nothing in the Constitution that prevented members of the Government from engaging in the debate as to whether the Constitution should be changed.
For an amendment to be presented to the people it must first pass the Oireachtas.
The court said it was then for the people to exercise their judgment on whether or not it should be carried.
It said members of the Government were entitled to engage in that process and it dismissed Ms Jordan's appeal on this issue.
The Supreme Court also dismissed Ms Jordan's appeal in relation to alleged irregularities in the voting register.
It said this issue had been assessed and decided by the High Court and the Court of Appeal and any further appeal would simply involve a reassessment of the evidence.
It also found it was difficult to disagree with the assessment by the Court of Appeal that the evidence put forward by Ms Jordan in relation to this issue was "flimsy".
The court also said there was no reason why costs should not be awarded against Ms Jordan.
Reporting Micheál Lehane and Orla O'Donnell