Quirke, from Breanshamore, Co Tipperary, had denied the murder of the 52-year old part-time DJ, known as 'Mr Moonlight', in June 2011.
However, after a fifteen-week trial, the jury delivered a ten to two majority verdict this afternoon.
Speaking outside court, Michelle Ryan said the verdict would not bring their father back, but the family hopes now that he is at rest.
She thanked the prosecution barristers in the case and gardaí in Tipperary, who she said worked "tirelessly".
Ms Ryan thanked the public for their support and kind words during what she described as "one of the hardest times of our lives".
She also thanked family friends, who she said they would have been lost without.
The Ryan family appealed to the media for privacy, as they come to terms with today’s verdict.
Earlier, in her victim impact statement, Ms Ryan said that the day her father went missing was the "day our lives and, the world as we knew it, was torn apart".
She said that the torment was constantly with the family.
Ms Ryan said when they close their eyes at night, the family pictured "daddy with fear in his eyes".
She said what happened to him "has consumed our lives completely".
Ms Ryan said they hope "daddy will now rest in peace", adding that he would never be forgotten.
She finished her victim impact statement speaking directly to her father, saying "so until we meet again Moonlight, just know how much you are loved and sorely missed by us every day."
