The Arizona State Fair Commission began planning for an "Arizona State Fairgrounds Exposition Center" as early as February 1960. The Commission envisioned an indoor facility which could be used during the State Fair as well as year-round. In 1964, Phoenix architect Leslie Mahoney, of the Lescher and Mahoney firm (designers of the Orpheum Theatre in downtown Phoenix among others) presented the commission with the final plans, and construction began that summer. Tucson architect Lew Place (son of University of Arizona chief campus architect Roy Place, and who later took over his father's firm) was also involved in the design. The structural engineering firm was T. Y. Lin International.
The unique saddle-shaped, tension-cable roof, supporting over 1,000 precast concrete panels, was considered innovative architectural engineering at the time. It may have been at least partially influenced by the equally innovative Dorton Arena at the North Carolina State Fair in Raleigh, completed in 1952. Veterans Memorial Coliseum also contains a series of murals by Phoenix artist Paul Coze. The design influenced later arenas' architecture, including the now-defunct Capital Centre in Landover, Maryland, and the Scotiabank Saddledome in Calgary, Alberta.