The Taoiseach, Mr Bertie Ahern, said the IRA statement was an "unparalleled breakthrough" that was of "profound importance" to the peace process.
He said the IRA had now done enough to satisfy General de Chastelain, but there was still an "enormous" amount of work remaining to be done.
"There have been several occasions over the last number of years where the word `historic' has been appropriate, and today's announcement clearly marks another, an unprecedented development," Mr Ahern said.
Mr Ahern paid tribute to the leaders of the IRA, who he said had made a brave and difficult decision in agreeing to decommission.
The Minister for Foreign Affairs, Mr Brian Cowen, said the statements from the IRA and the International Commission on decommissioning heralded a new era in the history of Ireland.
"This is a moment for political leaders to be responsive and generous. The reaction to decommissioning will be as important as decommissioning itself," he said.
"It is imperative that politics is made to work and that the nightmarish scenes like those from north Belfast are consigned forever to the pages of history."
"We must harness the new energy that has been released by today's developments and begin a new, dynamic era on this island at all levels, based on partnership, equality and mutual respect.
"We simply cannot afford to let this opportunity slip."
Mr Michael Noonan, the leader of Fine Gael, said he believed decommissioning had "already occurred" and that General de Chastelain would be confirming that "before too long".
"What we had was the Good Friday Agreement, there is an opportunity now to make it the Good Friday Settlement.
"Now that [decommissioning] has happened, it seems to me that there is no difference in principal between putting some arms beyond use and putting all arms beyond use."
Mr Ruairí Quinn, the leader of the Labour Party, said we are now witnessing events of "historic proportions."
He said all parties must now intensify efforts to overcome the "distrust and sectarianism that has bedevilled Northern Ireland for so long."
There is a particular obligation on the loyalist paramilitaries to honour the statements made that they would follow suit if the IRA started decommissioning.
