Walter Stone spent the first fourteen years of his life in Orange, New South Wales, before moving to Sydney where his father pursued a declining career as a bookmaker. After completing his education at the Parramatta Boys High School, he was articled to a solicitor, but after the solicitor's death he held a number of depression-era jobs such as rent collector and door-to-door salesman. Partial deafness kept him out of the military during the Second World War. He worked as a clerk for General Electric and continued that occupation with another company after the war until 1956.
Stone, a bibliophile from an early age, was a founding member of the Book Collectors' Society of Australia, editing and printing the organ of the society, Biblionews, for the rest of his life. Acting on his interest in book production, he bought his first press in 1951. During the next decade he produced a number of works, including Dulcie Deamer's poem 'Blue Centaur', P. R. Stephensen's Kookaburras and Satyrs (1954) and R. D. FitzGerald's poem of a convict-flogging, 'The Wind at Your Door' (1959). These titles established him as a fine printer and led to more than 100 such publications by 1981. He also printed and was general editor of the series Studies in Australian Bibliography (1954-1978) which recorded the publications of such writers as Henry Lawson, Joseph Furphy, John Shaw Neilson, Rolf Boldrewood, Christopher Brennan, Hugh McCrae, Marcus Clarke and several members of the Lindsay family.
Stone was an influential member of many organisations, including the Australian Society of Authors, the National Book Council and the Christopher Brennan Society. He actively campaigned with others for a Chair in Australian literature at the University of Sydney. A member of the Sydney Branch of the English Association, Stone edited the journal Southerly for one year in 1961 and printed the magazine at his Wentworth Press from 1962. He was also friend to many libraries, including the University of Sydney, La Trobe, the State Library of Victoria and the Fryer Library at the University of Queensland. For the latter, he was instrumental in acquiring the important Hayes Collection of Australian literature.
Walter Stone's contribution to Australian literature was recognised with an OAM in June 1981. Suffering from a long illness, he died two months later.