Liam Adams has been found guilty of ten counts of child sex abuse against his daughter Áine.
The jury at Belfast Crown Court found him guilty by a majority decision of 11-1 after deliberating for over five hours.
Adams, who is a brother of Sinn Féin President Gerry Adams, was convicted on three counts of rape, three counts of gross indecency and four counts of indecent assault.
The 58-year-old, from Bernagh Drive in west Belfast, had denied the charges.
The offences took place between March 1977 and 1983 when Ms Adams was between four and nine years old.
Ms Adams, who had waived her right to anonymity, sat in the public gallery with her mother and sister as the verdicts were read out.
In a statement afterwards, she said she did not consider the guilty verdicts against her father as a cause for celebration.
However, she said she could now get on with her life and lay to rest the memories of an abused childhood.
After his conviction, Adams was remanded in custody and it is expected he will be sentenced in four weeks' time.
Reacting to the verdict tonight, Gerry Adams said the trial has been "a distressing ordeal" for all of his family and for his niece Áine.
He said the family now requested the media to respect their right to space and privacy. He also thanked "the many people who have sent messages of support and solidarity".