He was the eldest son of John Matthew Conolly and Ellen J Conolly of Cranagh Hill, Coleraine, Co. Londonderry.
In 1901 the family are living in house 4, Castletoodry, Bannbrook, Co. Londonderry. By 1911 the property is known as house 8, Castletoodry, Bannbrook, Co. Londonderry.
He was known as Harry and was educated at Coleraine Acedemical Institution
The Belfast News Letter of 5th September 1916 reports:
2nd Lieutenant J H Connolly's name is recorded on the Queen's University Officer's Training Corps War Memorial.