Henry Arthur Johnson was born in Wheatley, Yorkshire, England in on 11 June 1903 and grew up in Doncaster, Yorkshire, England. He was the son of the Doncaster architect Thomas Henry Johnson (c.1872-1937). After studying at the Bartlett School of Architecture, University College, London, he returned to Doncaster and in the early 1920s formed the architectural partnership T. H. Johnson & Son with his father.
Following the death of his father in 1937, H. A. Johnson continued the practice with the title unchanged for some years. He was subsequently in partnership with William Crabtree (1905-1991) as Johnson & Crabtree at 20 Priory Place, Doncaster and 8 Robert Adam Street, London. The partnership was dissolved in 1952.
Johnson was an RIBA Donaldson Medalist in 1924-25. He was elected an Associate of the Royal Institute of British Architects (ARIBA) in 1927 and a Fellow of the Royal Institute of British Architects (FRIBA) in 1934.
Johnson died on 28 May 1988. His address at the time of his death was Carburton Grange, Worksop, Nottinghamshire
Notable among buildings designed by H. A. Johnson was the Co-operative Emporium (1938-40) at St. Sepulchre Gate, Doncaster, Yorkshire
Harwood, Elain. Art Deco Britain: Buildings of the interwar years. London: Batsford, 2019.