Morrissey was born in Mallow, County Cork (where his mother was from) but was raised in the Bronx, New York, where his parents worked. When he was aged 10, the family returned to Ireland to his father's native home of Clare. They settled in Mullagh. Later, Morrissey went on to study at St Flannan's College in Ennis and then University College Cork (UCC) in Cork where he studied medicine for three years before switching to microbiology and physics. He then did a master's in education at NUI Galway to become a teacher.