On Monday, a US Supreme Court judge upheld the ruling that the recordings, carried out under the supervision of Boston College researchers Ed Moloney and Anthony McIntyre, should be handed over to the authorities.
The discussions, which began in 2001, with republican and loyalist paramilitaries formed part of an oral history of the Troubles.
Ex-IRA member Dolours Price was one of the interviewees, and it is claimed the former prisoner discussed the disappearance of Jean McConville.
The mother of ten was abducted and murdered by the IRA in the 1972. Her body was recovered more than 30 years later.
The interviews were conducted under the assurance that the tapes would not be made public while the subjects were still alive. Price was found dead at her home in Dublin in January this year.
Former IRA member Brendan Hughes, who also took part in the project, died in 2008.
Authorities investigating Mrs McConville's disappearance had called for the US government to subpoena the documents, invoking a treaty between the UK and USA.
But Moloney and McIntyre - himself a former IRA volunteer-turned-writer - had argued that the tapes should be withheld under the First Amendment.
On Monday, an American court refused to hear an appeal lodged by Moloney and McIntyre. A further court ruling on the release of material involving different interviewees is due.