His parents worked as fruiterers in their family business at Bankstown until relocating to Coolangatta on the Gold Coast in 1967.

Having ministered as a deacon at All Saints Parish Albany Creek, he was ordained priest on 29 November 1991 at the Cathedral of St Stephen, Brisbane by Archbishop Francis Roberts Rush.

[8] Randazzo was appointed on 24 June 2016, along with Richard Umbers, by Pope Francis to be a new auxiliary bishop of the Archdiocese of Sydney.

In February 2023, Randazzo was elected president of the Federation of Catholic Bishops Conferences of Oceania for a four year term.

[9] In April, 2023, he was named Apostolic Administrator of the Personal Ordinariate of Our Lady of the Southern Cross, effective 1 July 2023, following the resignation of Monsignor Carl Reid.