Liam Adams, 58, from Bearnagh Drive in west Belfast, had denied all 10 charges against him.
After deliberating for over four hours on Tuesday, the jury of nine men and three women reached a 11-to-one majority verdict at Belfast Crown Court.
Adams was found guilty of three counts of rape, three counts of gross indecency and four counts of indecent assault carried out over a six-year period between March 1977 and 1983.
The offences against Aine Adams, who waived her right to anonymity, happened between the ages of four and nine years old.
Surrounded by her family, she wept in court as she heard the verdict.
On the other side of the public gallery, Adams's second wife Bronagh and their daughter Claire, who gave evidence in his defence, also cried.
Adams nodded to them as he was led to the cells.
He was remanded into custody to await sentence on 5 November.
During the trial Ms Adams gave graphic details of the abuse, and told the court the first time she remembered being raped was when her mother was in hospital giving birth to her younger brother in 1977.
In another incident she was raped by her father at a flat on Belfast's Antrim Road while her brother was asleep in the bed beside her.
Adams gave evidence in his defence and denied the abuse took place, dismissing it as "absolute rubbish".
I can now begin my life at 40 and lay to rest the memory of the five-year-old girl who was abused.
In a statement read out on her behalf outside court, Ms Adams said she could finally begin to move on after a long and hard road to achieve justice.
"I do not see this verdict as a victory or a celebration as it has taken its toll and has caused hurt, heartache and anguish for all those involved," her statement said.
She went on to thank her family for "their support and understanding". She also thanked the media for helping her "to tell (her) story and for the courtesy and respect they have shown throughout the trial".
"I would now ask for some privacy for myself and my family to reflect and heal from recent trying times."
The allegations were first made public in a UTV Insight documentary in 2009, when Aine Adams, then Tyrell, first waived her right to anonymity.
Ms Adams told UTV she had reported the abuse to police in 1987 but had later dropped the case.
The documentary also featured Sinn Féin President Gerry Adams, who said he believed his niece's allegations.
During a first trial earlier this year, which was abandoned for legal reasons, the former west Belfast MP claimed Liam Adams had confessed to him in 2000, but rejected claims he had also admitted the offences at an earlier meeting in Buncrana, Co Donegal.
However, Mr Adams was not called during this second trial to give evidence on behalf of the prosecution, something which was not lost in the minds of the jury.
A short time before delivering their verdict they sent a note into court seeking an explanation. In the note they asked for a reason why "Gerry Adams has not given evidence in this case as he is such a prominent figure throughout".
Judge Philpott told the jury simply that they should consider the case only on the evidence given to them in court, and not to speculate on any other matters.
On Tuesday evening, Gerry Adams described the trial of his brother as "tough".
"This has been a difficult and distressing ordeal for all my family and for my niece Aine," the politician said.
"I would ask the media to respect our right to space and privacy.
"I thank the many people who have sent messages of support and solidarity."