The former IRA leader who famously led a split from Sinn Fein has died aged 80.
In 1973, O Bradaigh was sentenced to six months in prison for membership of the Provisional IRA.
More than a decade later, he set up Republican Sinn Fein after disagreeing with the direction he believed Gerry Adams and Martin McGuinness were taking the party.
A republican fundamentalist all his life, O Bradaigh fell out with mainstream Sinn Fein over a decision to enter the Irish parliament if elected, thus ending the party's policy of abstention.
He believed armed struggle was valid as long as the British remained in Northern Ireland and in recent years made headlines after failing to condemn the 2009 Continuity IRA murder of Constable Stephen Carroll in Craigavon.
Last night, Gerry Adams spoke of his "sadness" at his death.
"On behalf of Sinn Fein, I want to extend my sincere condolences to his family and friends," he said. "Whatever differences we may have shared on political matters Ruairi was a life-long activist who was committed to his principles."
Des Dalton, his successor as president of Republican Sinn Fein, said he was a "towering figure of Irish republicanism in the latter half of the 20th century".
"He came to embody the very essence of the republican tradition, setting the very highest standards of commitment, duty, honour and loyalty to the cause of Irish freedom," said Mr Dalton.
Originally from Co Longford, O Bradaigh's father, Matt Brady, died when he was 10. He was an IRA man who suffered badly from injuries inflicted in 1919 by the Royal Irish Constabulary.
Educated at St Mel's College, Longford, and University College Dublin, O Bradaigh graduated in commerce and with an Irish language-teaching certificate. He became a teacher at Roscommon vocational school, resigning during periods in prison.
O Bradaigh was elected a TD while in prison for IRA activities in the 1950s. He had made it clear that had he been free he would have refused to go to the Dail and take part in its activities. For Mr O Bradaigh the only valid Dail was the one briefly established after the 1918 general election when the people of Ireland, north and south, voted on the same day.
The IRA veteran believed armed struggle was valid as long as the British remained in Northern Ireland and never denied that he was at one time chief of staff.
He also regarded the IRA ceasefire, the Good Friday Agreement and Martin McGuinness becoming deputy First Minister in a power-sharing government as a betrayal.