Morgan was born in Dublin and brought up in Rush, where his father was from. His mother is English. He learnt to play cricket at Rush Cricket Club, where his father, Jody, was Third XI captain. He was educated at the Catholic University School on Leeson Street, where he played in three Leinster Senior Schools Cup champion teams. In his early teens Morgan played hurling twice a week and this helped, to some degree, to develop his skills as a batsman, particularly as the grip for hurling is the same as for the reverse sweep. .