Crossan was born on February 17, 1934, in Nenagh, County Tipperary, Ireland. Though his father was a banker, Crossan was steeped in the rural Irish life, which he experienced through frequent visits to the home of his paternal grandparents. Upon graduation from St Eunan's College, a boarding high school, in 1950, Crossan joined the Servites, a Catholic religious order, and moved to the United States. He was trained at Stonebridge Seminary, Lake Bluff, Illinois, then ordained a priest in 1957. Crossan returned to Ireland, where he earned his Doctor of Divinity degree in 1959 at St Patrick's College, Maynooth, the Irish national seminary. He then completed two more years of study in biblical languages at the Pontifical Biblical Institute in Rome. In 1965 Crossan began two additional years of study (in archaeology) at the Ecole Biblique in Jordanian East Jerusalem. During this time, he travelled through several countries in the region, escaping just days before the outbreak of the Six-Day War of 1967.