Also included are convicted IRA murderers Kevin Barry Artt and Jim Smith, who were among 38 prisoners who escaped from the Maze Prison, near Belfast, in 1983 in the largest jailbreak in British history.
It applies to 21 cases dating back 20 years and means the government will not press for the return of fugitives who escaped from prison, and fled to other countries, before finishing their sentences.
Northern Ireland Secretary Peter Mandelson made the announcement on Friday, and said it was "clearly anomalous" to pursue such a course for people who would have little, if any, of their original sentence left.
However, he said it did not amount to an amnesty.
"I do not believe that it would not be proportionate or in the public interest to continue to pursue such cases," he said.
"I do not under-estimate the hurt this decision may cause the victims of those whose extradition will no longer be pursued, and the onus it places on all of use to ensure that the Good Friday Agreement does result in a permanent peace in which there are no more victims."
The new ruling would apply to the likes of IRA double murderer Liam Averill, who escaped from the Maze prison dressed as a woman in December 1997, and Diarmuid Finucane, the brother of the murdered Belfast solicitor Pat Finucane.
Also included are convicted IRA murderers Kevin Barry Artt and Jim Smith, who were among 38 prisoners who escaped from the Maze Prison, near Belfast, in 1983 in the largest jailbreak in British history.
They were arrested in California between 1992 and 1994 but, in 1998, were granted bail pending the men's hearing on their applications to stay in the US.
Mr Mandelson said if any individuals wished to benefit from the early release scheme, they would be able to return to Northern Ireland and make an application to the Sentence Review Commissioners.
'Absolute disgrace'
The ruling does not apply to those who have not been convicted of any offence - like the Harrods bomb suspect Evelyn Glenholmes who avoided extradition from the Republic in a high-profile case.
The move has been described as an "absolute disgrace" by the Ulster Unionist Jim Rodgers.
He said the government was "determined to give every concession possible to Sinn Fein/IRA."
Ian Paisley Junior of the Democratic Unionist Party also criticised the decision
"Here we have prisoners that should be captured and put behind bars. They are benefiting from the peace process, something they have contributed nothing to, " he said.
"I can't believe Peter Mandelson's decision. It's as if he wants to see this process extinguished. This is the nail in the coffin for the Agreement.
But the decision has been welcomed by Sinn Fein's Alex Maskey.
"This is a useful first step in tackling this important issue. It will undoubtedly come as a relief to those individuals and their families who have lived with the threat of extradition for many years."
Sinn Fein has, in the past, urged the British Government to drop its extradition cases "in the spirit of the Good Friday Agreement and the logic of the peace process".