Members of the Conlon and Maguire families were jailed in connection with Irish Republican Army bombings in Guildford and Woolwich in England in 1974. One attack killed five people and injured 54 others.
"I am very sorry that they were subject to such an ordeal and injustice," Blair said in a statement. "That is why I am making this apology today, they deserve to be completely and publicly exonerated."
Guiseppe Conlon and his son, Gerry, were imprisoned for the bombings. Guiseppe Conlon died in prison in 1980, while Gerry Conlon was released after serving 15 years.
The 1993 film earned seven Oscar nominations. Pete Postlethwaite portrayed Guiseppe Conlon and Daniel-Day Lewis portrayed Gerry.
Blair set a precedent for such apologies soon after taking office in 1997, when he offered a statement of regret for British policy during the 1845-1852 potato famine, during which 1 million people died in Ireland and another 2 million fled to Britain or North America.
Blair's gesture Wednesday came during the latest deadlock in Northern Ireland's long-running peace process and with pressure mounting on Sinn Fein, the IRA-linked party, over the outlawed group's alleged $50 million robbery of a Belfast bank — the biggest cash theft in history.
Irish Prime Minister Bertie has said he believes the IRA committed the Dec. 20 raid on Northern Bank and that senior figures in Sinn Fein authorized it. The IRA has denied involvement, and police have made no arrests and recovered none of the cash.