The British Prime Minister, Mr Tony Blair, has issued a public apology to the Conlon and Maguire families for their wrongful imprisonment for the IRA bomb attacks in Guildford and Woolwich in 1974.
In a televised address, Mr Blair said "I am very sorry that they were subject to such an ordeal and injustice ... That is why I am making this apology today - they deserve to be completely and publicly exonerated."
Mr Blair met with representatives of both families after making the statement.
Mr Blair apologised for the wrongful imprisonment of Mr Conlon and his father, Guiseppe, who died while wrongly imprisoned for a bombing in Guildford in 1974.
Mr Gerry Conlon, who spent 15 years in jail after his wrongful conviction, had hoped that Mr Blair would make his apology in the Commons chamber during Prime Minister's Questions this afternoon.
However, the apology failed to materialise during question time as expected. The SDLP's Eddie McGrady was expected to prompt Mr Blair to make the apology but was not given the opportunity to do so by the speaker of the house.
Speaking on his arrival at the House of Commons in London this morning, Mr Conlon said the case remains "a stain on the character of British justice."
Gerry Conlon on his release outside the Old Bailey in London
Mr Conlon - along with Mr Paddy Armstrong, Mr Paul Hill and Ms Carole Richardson - were arrested in 1974 and wrongfully jailed for an IRA bomb attack on the Horse and Groom pub in Guildford.
The blast killed five people - four soldiers and a civilian. The prisoners became known as the Guildford Four.
On his arrival at the House of Commons this morning, Mr Conlon told journalists: "This has been a stain on the character of British justice. "Today, hopefully, Tony Blair is going to remove part of that stain, and the stigma that has been attached to me and my family."
Mr Conlon was asked whether anything could make up for the years he spent in jail. He said: "No, no, but hopefully this will go some way to removing doubt that exists in people."
Mr Conlon said the Government owed a debt to himself and others wrongly jailed. "Everyone who was arrested around about that time and went to prison has had their lives shattered. "If you can destroy them, you have the moral obligation when they do come out and that is not forthcoming.
"We hope that the assistance and the medical facilities that are available to others will be made available to us." Mr Conlon added: "This apology is so important, not just for me but for my mother, my sisters, my nieces, my nephews, because this has seeped down the generations."
The Conlon family has been seeking a public apology from the British Government for the miscarriage of justice and have compiled a petition which has been signed by tens of thousands of people.
Mr Conlon's father and members of Mrs Annie Maguire's family were also later arrested and jailed for the attack and other bombings in Woolwich, south east London after they were allegedly identified as being involved in the bomb plot in confessions extracted by the police.
Mr Guiseppe Conlon died in prison while serving his sentence in January 1980. In October 1989 the Court of Appeal quashed the sentences of the Guildford Four after doubts were raised about the police evidence.
In June 1991, the Court of Appeal also overturned the sentences on the Maguires and Guiseppe Conlon.