In a video-taped statement released by Downing Street on Wednesday, Blair admitted the jailing of 11 innocent people for bomb blasts caused by the IRA was wrong.
The PM said sorry for the plight of the prisoners who became known as the Guilford Four and Maguire Seven, who spent up to 14 years in prison for crimes they did not commit.
"I am very sorry that they were subject to such an ordeal and injustice," said Blair, who had intended to make the apology in parliament earlier on Wednesday but was not able to do due to House of Commons procedures.
The cases of the Guilford Four and the Maguire Seven became world-famous through Oscar-winning 1993 film In the Name of the Father, starring Daniel Day-Lewis as Gerry Conlon.
Conlon was among four people arrested in 1974 and jailed for an Irish Republican Army (IRA) bomb attack on a pub frequented by British soldiers in Guilford, just outside London, in which five people died.
His father Guiseppe was one of seven others jailed in connection with that attack and another bombing in south east London. He died in prison in 1980.