Northern Ireland secretary Chris Heaton-Harris made a Commons statement on Thursday confirming he intends to establish the inquiry in response to a court judgment that directed the Government to establish some form of investigation.
Michael Gallagher, whose son Aiden died in the Real IRA bombing, took the legal challenge that resulted in the judge directing the state to act.
The dissident republican bomb exploded in the Co Tyrone town on August 15, 1998, killing 29 people, including a woman pregnant with twins. Hundreds more were injured.
Mr Heaton-Harris said he had listened to representations of those families affected by the atrocity alongside other factors, including its independence, cost to public purse and how best to "allay wider public concern".
Speaking in the Commons, Mr Heaton-Harris said: "I intend to establish an independent statutory inquiry into the Omagh bombing.
"I have informed Mr Gallagher and members of the Omagh Support and Self Help Group, as well as representatives of Families Moving On of this decision.
"The inquiry will focus specifically on the four grounds which the court held as giving rise to plausible arguments that the bombing could have been prevented.
"The inquiry will also need to take account of the findings of previous investigations to avoid duplication."
Mr Heaton-Harris said he accepted this was a "significant" decision. Mr Gallagher welcomed the announcement.
"The Secretary of State has given us everything that we have asked for, and we're very appreciative of that," he said.
"It's still sinking in, to be honest, I think it's going to be a long time to come to terms with the fact that we're going to hopefully get the answers that we need and we can move on."
Mr Gallagher said the probe announced did amount to a full public inquiry.
"My understanding is that it is a public inquiry, it's a judicial inquiry with powers of investigation and that's exactly what we wanted," he said.
"This is not a case of deflecting the blame from those who are responsible – that was the criminal terrorists who planned, prepared and delivered this bomb into Omagh. What we're looking at is the failings of the people that are there to protect us."
He said reliving the events of Omagh through the inquiry would be "difficult" and "painful" for the families, but added: "If we don't have this process, for the rest of our lives we're going to be wondering 'what if'."
Labour welcomed the decision to open the inquiry, and said the Republic of Ireland had "a moral obligation to start their own investigation".
But shadow Northern Ireland secretary Peter Kyle said the move clashed "with the Government's overall approach to legacy issues" as set out in the Northern Ireland Troubles (Legacy and Reconciliation) Bill.
He said: "The Secretary of State has put Omagh families at the heart of today's decision. I'm worried that other victims of atrocities during the Troubles will be watching and wondering why their loved ones are not being treated in a similar way?"