McElhone was born in Sydney, the son of New South Wales politician John McElhone and his wife Mary Jane (née Browne). His brother, William Percy McElhone (1871–1932), also served as Lord Mayor of Sydney in 1922. He married Eva Catherine Walshe in 1897. The couple had four children; one of his sons, John Fitzroy McElhone (1899–1970), became a Sydney aldermen in 1946, serving until 1953.[2]
McElhone died on 17 June 1946 at Gloucester House, Sydney, aged 77.[2] In 1950, a park in Elizabeth Bay, Sydney, Arthur McElhone Reserve, was named in honour of him.[1][3]