Knox was born in Bayswater, Western Australia. He was a son of Irish–born John Knox and his wife Alice Emily, née Walsh. Attending Catholic schools in Perth, Knox applied to the archdiocese to study for the priesthood, but was rejected because it was cheaper to recruit and educate priests in Ireland. He successfully applied to become a priest at the BenedictineTerritorial Abbey of New Norcia and completed his secondary schooling at St Ildephonsus' College before entering the seminary in 1936. By September that year, he transferred to the Pontifical Urbanian Athenaeum in Rome. Ordained priest on 22 December 1941, he pursued postgraduate studies, obtaining doctorates in theology and canon law. Unable to return to Australia during World War II, he had been assigned to Propaganda College staff, becoming a vice-rector in 1945. He served as a staff member of the Vatican Secretariat of State from 1948 until 1950. He was also a staff member of Vatican Radio for a year between 1949 and 1950 and appointed to the rank of monsignor on 22 July 1950. He was Secretary to the Apostolic Delegate in Japan from 1950 until 1953.
Episcopate
appointed him Titular Archbishop of Melitene and apostolic delegate in British Africa on 20 July 1953. He was consecrated in November that year in Rome by Cardinal Celso Costantini. He was Internuncio in India and apostolic delegate in Burma and Ceylon from 1957 where he was involved with the expansion of Mother Teresa's Missionaries of Charity. He attended the Second Vatican Council in Rome. On 13 April 1967, with no direct pastoral experience, Knox was appointed as the fifth Archbishop of Melbourne. Following decrees of the Second Vatican Council, in 1970 Knox approved the extension of St Patrick's Cathedral's sanctuary into the transept crossing to provide the space required for the reformed liturgical rites. The new sanctuary worked admirably for the many ceremonies of the 40th International Eucharistic Congress held in Melbourne in February 1973. Knox reorganised the structure of the archdiocese, establishing four regions headed by auxiliary bishops, the creation of 12 archdiocesan departments headed by episcopal vicars as well as the establishment of a Senate of Priests and other advisory bodies. During his episcopacy as archbishop, Knox was also instrumental in the creation of the Melbourne College of Divinity and later, some of the constituent parts which became the Australian Catholic University.