Kelly was born in Bearnacraugh,
Aughrim,
Ballinasloe, County Galway, Ireland, on 31 August 1894. He received his early education at Aughrim Primary School and later attended "The Pines" College in Ballinasloe, now known as
St Joseph's, Garbally Park. He temporarily paused his studies to assist on the family farm before resuming them in 1915 at the SMA apostolic school in
Wilton, Cork. He then studied philosophy and theology at the SMA seminary on Blackrock Road, Cork. Kelly was received into the Society of African Missions on 1 November 1918 and ordained a priest on 29 June 1921 by Bishop Thomas Broderick, Vicar Apostolic of Western Nigeria. ==Missionary work in Nigeria==