Taoiseach Leo Varadkar has said Ireland "will not be found wanting" in any inquiry into the Omagh bomb.
He described the Omagh atrocity as a "terrible crime committed by the Real IRA, an act of barbarous inhumanity".
The dissident republican bomb exploded in the Co Tyrone town on 15 August 1998, killing 29 people, including a woman pregnant with twins. Hundreds more were injured.
Northern Ireland Secretary Chris Heaton-Harris confirmed he intends to establish the inquiry in response to a court judgment that directed the UK government to establish some form of investigation.
Speaking ahead of the announcement, Mr Varadkar said: "It is important that those families that are still suffering today get the truth that they need and they deserve.
"There was probably a cross-border element to this crime and we are going to sit down with the UK authorities and work out how we can contribute to that.
"We certainly won't be found wanting in terms of making sure that any aspect of this that happened in our jurisdiction, on our side of the border is fully investigated as well and we will have to agree the right mechanisms to do that."
Tánaiste Micheál Martin said today's announcement "serves as a reminder of the need to deal effectively with the legacy of the past".
In a statement, the Minister for Foreign Affairs and Minister for Defence added: "What happened in Omagh was a heinous attack, carried out by people with no respect for the lives of others or for democracy on this island.
"My thoughts are with the families of those murdered and with the survivors.
"The announcement by Secretary of State for Northern Ireland Chris Heaton-Harris is welcome.
"I spoke with him last evening and he confirmed his intention to make today's statement to me.
"We now await further detail from the UK government, in particular on the terms of reference for their inquiry.
"I look forward to receiving that detail and then consulting with my Cabinet colleagues, in particular the Minister for Justice, about the next steps.
"While welcoming today’s announcement, it also serves as a reminder of the need to deal effectively with the legacy of the past, in a manner which advances the fundamental goal of reconciliation."
Minister for Justice Simon Harris said the Government will consider if there is any action it is required to take, following the announcement on establishing an inquiry.
Mr Harris said the Government "will now take time to consider that [decision], to see if there's any action that we're required to take on this side of the jurisdiction."
He said the Government will also consider if there is "any action that we could take that would add any additional benefit ... to the work announced today by the UK government," adding that he will engage with his Cabinet colleagues in relation to the matter.
'Everything that we wanted'
Michael Gallagher, whose son Aiden died in the bombing, took the legal challenge that resulted in the judge directing the state to act.
Speaking on RTÉ's News at One, he said the inquiry was "everything that we wanted".
He said: "I thought that it was something that I would never hear.
"It was unbelievable - the fact that we've got a judicial inquiry with powers of investigation. That's exactly what is needed.
"We obviously need to work out the terms of reference with the government, but I think it's fantastic news.
"The Secretary of State did stick to his word. He said that he would let us know shortly after Christmas.
"It's everything that we wanted, but, of course, it's in the details that we have to work out from here on in.
"It is a very important step forward."
Mr Gallagher also said that he has told the Irish Government that there "will be embarrassments" for it in the inquiry.
He said: "Make no doubt about it, there will be embarrassments here for the British government and there will also be embarrassments for the Irish Government and I told the Taoiseach that on 5 February last year."
He said that the Irish and British governments are "not our enemy," adding "we know who our enemy is".
He said the question of how intelligence was managed in the lead-up to the bombing is a "central" question that will need to be probed during the inquiry.
"We know from our experience that there was a huge amount of raw intelligence available through a number of agents and also there were warnings, so all of that needs to be looked at carefully."
He said that there is a "very strong cross-border element" to the Omagh bombing.
Mr Gallagher added: "We need and it's important that we have the input from the Irish authorities.
"We have a certain amount of information and the Irish Government would have a lot more information and I think it's important for us."
Families of pub bombings left 'wondering', says shadow NI secretary
Meanwhile, the UK's Labour party has said that families of the Birmingham pub bombings' victims will be left "watching and wondering" why the government has not ordered a public inquiry into the 1974 blasts after having done so for the Omagh attack.
Welcoming the British's government's move, shadow Northern Ireland Secretary Peter Kyle spoke of "contradictions" and "clash" in the government's approach to victims of different atrocities during the Troubles, and after the signing of the Good Friday Agreement in 1998.
Mr Kyle referenced the Birmingham pub bombings, in which 21 people died and more than 200 were injured after twin blasts on 21 November 1974.
The victims' families, through the Justice4the21 campaign group, have been pleading for a public inquiry into the deaths of their loved ones for years.
New inquests into the victims' deaths were held in the city in 2019, but the issue of perpetrators was excluded by the coroner, leading the families to claim they had been left with many unanswered questions.
Speaking in the House of Commons, Mr Kyle said: "The fact the (Northern Ireland) secretary is calling for this inquiry does clash with the government's overall approach to legacy issues.
"Victims are already noticing contradictions in the government's approach to legacy issues."
Mr Kyle said he believed the Northern Ireland secretary to be "a decent man", adding Mr Heaton-Harris "needs to be certain that it will provide the same comfort and answers to all victims that he is offering family the families of Omagh today".
Responding, Mr Heaton-Harris said: "I actually do believe that we are being consistent.
"What has happened is that for hundreds if not thousands of families (in the) 25 years since the Troubles ceased, and the Belfast Good Friday agreement came into effect - there's been no justice and no information about what's happened."
Additional reporting PA
