Morant was born in Ireland 8 August 1837. There is a record of his baptism in the Parish of Farnborough, Hampshire on 20 January 1838, with parents George and Lydia Morant  His father was the elder son of George Morant, of Shirley House, Carrickmacross, and Lydia Hemphill, daughter of John Hemphill, of Rathkeany, Co. Tipperary. Morant’s father served in the Grenadier Guards, and was a justice of the peace. The senior line of the Morant family (the elder George Morant being grandson of the former head of the family) lived at Brockenhurst, Hampshire, and claimed Norman descent tracing back from William de Moraunt, of Moraunt’s Court, in Kent, who was high sheriff of that county in 1337 and 1338, during the reign of King Edward III. They were later resident in Jamaica, and owned plantations there.
Morant married, in 1866, Sophia Georgina Eyres, younger daughter of Colonel George William Eyres, of the Grenadier Guards. Lady Morant died in 1911, and he died ten years later, on 13 February 1921. Morant was survived by three sons and four daughters. One of Morant’s sons, Edgar Robert Morant, D.S.O. (1874-1931) also served as a captain of the Royal Navy. One daughter, Sybil Mary Morant, married the publisher James Blackwood (1878-1951), while another, Aileen Morant (d 1969), married another Royal Navy officer, Captain Llewellyn Evan Hugh Llewellyn (1879-1970). The controversial British-Australian war criminal Harry Harbord “Breaker” Morant claimed to be his illegitimate son, but two months after Morant’s execution, Admiral Morant issued a statement denying that Morant was his son or anyway related to him. The younger Morant was actually the son of Edwin and Catherine Murrant.