Hackett, nicknamed "Shan", was born in Perth, Western Australia. His Irish Australian father, also named Sir John Winthrop Hackett (1848–1916), originally from Tipperary, was educated at Trinity College, Dublin (B.A., 1871; M.A., 1874), and he emigrated to Australia in 1875, eventually settling in Western Australia in 1882, where he became a newspaper proprietor and editor and a politician. His mother was Deborah Drake-Brockman. Her parents were prominent members of Western Australian society: Grace Bussell, famous for rescuing shipwreck survivors as a teenager and Frederick Slade Drake-Brockman, a prominent surveyor and explorer. Deborah had three sisters and three brothers.