Dolours Price was found dead at her home in Malahide, north Dublin, on Wednesday night, with detectives claiming her death is not being treated as suspicious.
The 62-year-old mother-of-two was also the former wife of actor Stephen Rea.
She was convicted, along with her sister Marian and leading Sinn Fein member Gerry Kelly, of the Provisional IRA car bombing in 1973 of London's Old Bailey courts in which one man died and more than 200 people were injured.
In recent years she had aligned herself with dissident republicans and was an outspoken critic of the IRA leadership and Sinn Fein President Gerry Adams.
Her death has reignited the transatlantic legal battle over secret testimony she gave to an American college about her time in the IRA.
Former IRA volunteer-turned-writer Anthony McIntyre interviewed Ms Price, and a number of other republican and loyalist paramilitaries, for a history project at Boston College in the US that began in 2001.
The interviewees were promised the confidential archived material would not be made public until after their deaths.
However, Ms Price had previously claimed to a Belfast newspaper that, during the recordings, she made allegations that Mr Adams personally ordered the abduction of several people in the 1970s, including Belfast mother-of-10 Jean McConville.
Mr Adams has always denied ever being a member of the IRA.
In 2011, the Police Service of Northern Ireland (PSNI) launched a legal bid to force the college to hand over the transcripts, as part of its investigation into the murder of Mrs McConville.
In media interviews, Ms Price claimed to have been the person who drove Mrs McConville to her death.
The researchers at Boston College fought the PSNI action, arguing that surrendering the transcripts would put lives at risk and compromise future oral history projects as a confidentiality agreement would have been broken.
Immediately after news of Ms Price's death emerged, there were reports in Ireland that the tapes would now be handed over.
Those close to Boston College's "Belfast Project" are said to believe the death of Ms Price means her recorded interviews will now simply be handed over as a matter of course.
According to the agreement the college made with the interviewees, their testimony would be kept secret and secure in the Burns Library on its main campus until after the contributors had died.
IRA commander Brendan Hughes's revelations about his role during the Troubles were later published in a book and formed the basis of a television documentary, along with those of the former UVF member and later leader of the Progressive Unionist Party, David Ervine.
Mr Adams said: "I want to extend my sincere condolences to her family and especially to her two sons, Danny and Oscar, and her sister Marian.
"I have known Dolours for a very long time. She endured great hardship during her time in prison in the 1970s, enduring a hunger strike which included force-feeding for over 200 days.
"In more recent years she has had many personal trials.
"I am sure all of those who knew Dolours will be very sad at the news of her death."
In later life Ms Price had problems with alcohol and prescription drugs.
Her sister, Marian Price, is currently in custody.
She was granted bail in May 2011 after being charged with supporting an illegal organisation. However, she was not released due to the then Secretary of State Owen Paterson's separate decision to revoke her early release licence.
She is accused of holding a speech for a masked man at a dissident rally on Easter Sunday 2011.
She has also been charged with providing property for the purposes of terrorism in relation to the murder of two soldiers at Massereene, Belfast, in 2009. She denies the charges.
The family of Dolours Price, who asked for their privacy to be respected, said they will release a statement later.