When Moran was 11 years old, he was left orphaned when both of his parents died. He went into the care of his uncle, then rector of the Irish College in Rome. There Moran attended a seminary and began his introduction into a life in the church.
Moran was an incredibly intelligent young man, and by the age of 25 was able to speak 10 languages, including ancient ones. His work with manuscripts is still highly valued in academic and ecclesiastical circles today. By 1886 he was appointed as secretary to the cardinal of Dublin, who just happened to be the same uncle who took him to Rome in the first place. He was also appointed Professor of Scripture at Cunliffe College in Dublin.
On the 22nd of December 1861, Moran was consecrated as coadjutor Bishop of Ossary, eventually taking the full title when his predecssor passed away. As Bishop of Ossary, he was highly vocal in his support for Home Rule and was consulted by Gladstone in the drafting of his Home Rule Bills.
On the 8th of September 1884, Moran arrived in Australia after being personall appointed by Pope Leo XIII to head the Archdiocese of Sydney. His title was now that of Cardinal-Priest, making him the first Australian Cardinal. He travelled extensively across Australia and New Zealand ordaining priests and consecrating churches and cathedrals.
Moran died in Sydney on the 17th of August 1911. His funeral was attended by approximately 250,000 people. He is buried in St Mary's Cathedral Sydney.