Legislation to allow for abortion in certain circumstances should be approved in the coming weeks.
It comes after the Supreme Court refused to allow a Dublin woman to appeal her challenge to May’s referendum result.
Joanna Jordan from Dún Laoghaire had taken the case in the lower courts, alleging the register of electors was overstated.
She also raised concerns over the participation of members of the Government in the Yes campaign.
The High Court had already rejected her application, and the Supreme Court will not allow her to appeal that decision.
Leo Varadkar says it means the Government can introduce the legislation soon, but it may be January before services are up and running.
The Taoiseach said: "That means that the Eighth Amendment can now be ratified and signed into law by the President, thus formally amending our constitution giving effect to what people voted for back in May.
"That allows us now as a government to bring forward the legislation to allow for abortion in Ireland in certain circumstances when the Dáil returns."
In a determination published today, the Supreme Court found it was "not satisfied that the constitutional threshold for leave to appeal has been met and refuses leave".
On the subject of alleged irregularities in the register of voters, the court suggested "it is difficult to disagree with the assessment made by the Court of Appeal of the evidence presented in this regard as being 'flimsy'".
It adds that settled case law "makes clear that members of the Government are entitled to engage" in the referendum process and debate.
