Osbiston was born in Crows Nest, New South Wales, to Charles Alan and Emily Florence "Bae" Osbiston, née Brigstocke of Brockley Farm, Mount Druitt, New South Wales. Osbiston attended "Shore School" and for much of his early life lived in Chatswood, Sydney. Prior to joining the British Ministry of Information, Osbiston worked for Cinesound in Sydney. Osbiston married Lyla Cranston of London, on 15 August 1942 in London. He was a cousin of Australian actor Max Osbiston (7 August 1914 – 12 March 1981).