His hiring marks an attempt by the agency to strengthen its creative offering.
Current creative director Damian Kirby, who has worked at Table 19 and co-founded the business, will now report to Wall. He will work across its range of clients including Sky, Carphone Warehouse and News International.
Before The Marketing Store, Wall worked at Billington Cartmell, Rapier and Rapp.
Matt Broekhuizen, managing partner of Table19, said: "This is a huge leap forward for us. Throughout his career, Graham has consistently delivered world-class creative. At the same time, he has an impressive track record of leading and inspiring others to go further and produce better work."
Wall added: "[Table19] are a young, dynamic company with a unique proposition, a clear vision of where they want to be and a determination to get there."