The brother of Sinn Fein president Gerry Adams will be extradited to Northern Ireland next month to face 18 allegations that he abused his daughter.
Liam Adams was remanded in custody in the Republic after losing a legal bid to appeal against his extradition.
The 56-year-old, who denies the abuse allegations made by Aine Tyrell, will be held for 15 days until the extradition order takes effect.Mr Adams will be then handed over to the Police Service of Northern Ireland within the following 10 days.
The defendant, who showed no emotion as the High Court ruling was made, hugged his other daughter Claire Smith before he was led away by prison officers.
Mr Justice John Edwards - who earlier ordered his extradition - said he would not allow an appeal to the Supreme Court. The judge added: "The court arrived at the decision, it is disposed not to certify any of the points raised as points of law or exceptional public importance."
Adams is accused of rape, indecent assault and gross indecency at various addresses in Belfast between March 1977 and March 1983, when the alleged victim was aged between four and 10.
His daughter Ms Tyrell, who has waived her right to anonymity, first lodged a complaint along with her mother Sarah Adams to police in Belfast on January 21, 1987. She claimed her father "would get into her bed and always do the same things to her".
The accused, whose last address was Bernagh Avenue in Belfast, denied the allegations when arrested in February 2007. The sex abuse claims became public in December 2009 when Ms Tyrell was featured in a television documentary.
Mr Justice Edwards told Adams any complaint over the legality of his detention over the next two weeks could be made to the High Court under Article 40 of the constitution.
The judge also ordered the state give Adams back his passport and that cash bonds be returned to his friend Sean Rooney and Ms Smith, who had guaranteed his bail on bonds of 7,500 euro each when he was arrested in March.