Mr Blair's apology and declaration that those jailed for the 1974 Guildford and Woolwich bombings deserved to be "completely and publicly exonerated" was what they had sought for years.
The apology was delivered in a TV statement in his office in the House of Commons and then in private to those wronged by the British legal system. He then shook their hands.
Mr Blair's spokesman said: "It was a meeting which nobody who was present will ever forget."
In a day of high drama and emotion, the Conlon and Maguire families travelled to Parliament expecting to hear Mr Blair deliver the apology during Prime Minister's Questions.
It didn't happen. SDLP South Down MP Eddie McGrady hovered on his seat trying to catch the Speaker's eye to ask the question which would have prompted the apology.
The Speaker didn't call him, apparently having ruled it was not an issue for the weekly question session. Immediately afterwards Mr Blair moved to Plan B and made a TV statement in his office before inviting the Conlons and Maguires in for a private meeting at which he read the statement again.
He said: "I'm very sorry that they were subject to such an ordeal and such an injustice. That's why I'm making this apology today. They deserve to be completely and publicly exonerated."
Gerry Conlon who along with Paddy Armstrong, Paul Hill and Carole Richardson became known as the Guildford Four after being arrested in 1974 for the bombing of the Horse and Groom pub in the town and jailed for life was delighted.
He said Mr Blair had spoken to them with "such sincerity".
"He went beyond what we thought he would, he took time to listen to everyone. He exceeded our expectations in apologising. He said it was long overdue.
"You could see he was moved by what people were saying. Tony Blair has healed rifts, he is helping to heal wounds. It's a day I never thought would come.
"Everyone has been affected by this, everyone has suffered trauma from it. And the good thing is that he has acknowledged it, and he accepts that we are in pain, that we are suffering terrible, terrible nightmares and terrible post-traumatic stress disorder."
Annie Maguire, speaking after her meeting with Mr Blair, said it was a "wonderful feeling" to have the apology and a weight had been lifted from her shoulders.
Taoiseach Bertie Ahern said he hoped the Blair apology would make up for many years of suffering for the Conlon family.
"I appreciate that Tony Blair has agreed to my request for this issue to be addressed."