Taoiseach Bertie Ahern said that today's IRA statement meant that "the war is over".
"The war is over, the IRA's armed campaign is over, paramilitarism is over and I believe that we can look to the future of peace and prosperity based on mutual trust and reconciliation and a final end to violence," said Mr Ahern.
Mr Ahern has said that the focus must now turn to completing the implementation of the Good Friday Agreement and ensuring IRA decommissioning is independently verified.
He said there would be difficult issues to address in order to move forward.
"These include policing, the end to loyalist paramilitary activity and the restoration of the political institutions."
He also ruled out any possibility of those jailed for the murder of Garda Gerry McCabe being released early or any amnesty being extended to those on the run in relation to the murder.
However, he did say that proposals for dealing with other "on the run" republicans would be formulated before Christmas.
Mr Ahern also ruled out the possibility of the political institutions being restored before decommissioning had been verified.
"Independent verification is vital to ensure that trust is restored."
Mr Ahern also said he was happy that the reference to "all other activities" in the IRA statement covered criminal activity. This is the phrase the two governments had used in Paragraph 13 of their Joint Declaration to cover criminality.
"I hope and believe that today marks the day when the tradition of violence finally comes to an end," said Mr Ahern.
"If the IRA's words are borne out by verifiable actions it will be a momentous and historic development."
He also said the victims of violence in the North should be remembered and he acknowledge that today would be a difficult day for their relatives.
Speaking to reporters at Downing Street, British Prime Minister Tony Blair welcomed the clarity of the IRA statement and said it paves the way for the restoration of the suspended institutions in Northern Ireland.
"I welcome the recognition that the only route to political change lies in exclusively peaceful and democratic means," he said. "It creates the circumstances in which the institutions can be revived."
"Unionism will want to know that these circumstances are permanent and verified, but if in time they are, proper devolved democratic government should be restored to Northern Ireland."
Mr Blair also said the instruction to IRA volunteers not to engage in any other activities whatsoever would "be taken as a forthright denunciation of any activity, paramilitary or criminal".
Hailing the statement as historic Mr Ahern said it met the public demands he made of Sinn Féin following their meeting in January of this year.
"I wanted to see decommissioning be dealt with, I wanted to see the IRA as a paramilitary organisation ceasing and I wanted to see that the issues as set out in the [two Government's] Joint Declaration were covered."
"This statement covers those points, there's no doubt about that."
The two governments have asked the Independent Monitoring Commission to produce an additional report in January 2006, three months after their next regular report.
"Verified acts of completion will provide a context in which we will expect all parties to work towards the full operation of the political institutions, including the Northern Ireland Assembly and Executive, and the North-South structures, at the earliest practicable date," Mr Ahern and Mr Blair said in the statement.
"We also expect all parties and community leaders to use their influence to bring loyalist paramilitary and criminal activity to an end, including the full decommissioning of weapons."