Houston snr is widely regarded as the father of Australia's Pentecostal movement, through his work with the Australian Assemblies of God, now known as Australian Christian Churches.
Hillsong has grown into one of Australia's biggest movements with 30,000 weekly churchgoers.
The Royal Commission into Institutional Responses to Child Sexual Abuse will also look at the response of Australian Christian Churches to allegations of child sexual abuse made against former church youth worker Jonathan Thomas Baldwin.
Baldwin was sentenced to eight years' jail in 2009 after being found guilty of molesting a teenage boy he met through his role as a youth pastor at a Sunshine Coast church.
Maroochydore District Court heard the abuse started in 2004 and continued for an 18-month period, occurring at a church sleepover, a car park near the church and during a Gold Coast holiday.
The royal commission will also examine the response of the Northside Christian College and the Northside Christian Centre, now Encompass Church, to allegations of child sexual abuse made against former teacher Kenneth Sandilands.
Encompass Church pastor John Spinella said the church welcomed the inquiry and said it was co-operating with royal commission staff.
"As a church we have recognised these past failures and take the opportunity to apologise for the suffering and pain endured by those who were abused," he said.
The public hearing will begin in Sydney on October 7.