Wallace Austin Greenen was born in East Cowes, Isle of Wight, Hampshire, England in 1887 and practised as an architect in Hampshire. He was in partnership or at least collaborated with architect Ernest Josiah Edwards Moore 1886-?) in c.1919. They participated in the Daily Mail Architects Competition for Workers' Homes in 1919. Their design was "Commended". From 1922 to the mid-1930s he was in partnership with Gordon Wallet Jackson (1885-1965) as Jackson & Greenen in Bournemouth, Hampshire [now Dorset] Edmonsham House, an apartment block in Orchard Street, Bournemouth designed by Jackson & Greenen in 1935 is described in Flats: Municipal and Private Enterprise (London: Ascot Gas Water Heaters Ltd., 1938 pp. 222-225)
Greenen was a Member of the Society of Architects (MSA) and was admitted a Licentiate of the Royal Institute of British Architects (LRIBA) in 1925. He was elected a Fellow of the Royal Institute of British Architects (FRIBA) in 1930, His address was given as 15, Leslie Road, Winton, Bournemouth, Hampshire [now Dorset] in 1923; 5, Yelverton Road, Bournemouth, Hampshire [now Dorset] in 1926; 5 & 7, Yelverton Road, Bournemouth, Hampshire [now Dorset]; and Hinton Buildings, Hinton Road, Bournemouth, Hampshire [now Dorset] in 1936. He died in Bournemouth on 17 February 1938.