The bank opend in 1913 as the London, City and Midland Bank who were bought by HSBC in 1999.
The building is Grade II listed, and Gails will reportedly utilise the high ceilings to create a mezzanine.
Andrew Shepherd, Director at AS Retail said: "We received a lot of interest in this fabulous building but GAIL’s are the perfect occupier to make use of this unique space. They were not phased by the listed nature of the building and we look forward to seeing how they transform the building over the coming weeks.”
Gail's bakery was co-founded by Israeli baker Gail Meija and businessman Ran Avidan, who owns the holding company associated with the brand.
In recent years, Gail's has undertaken a rapid expansion, hitting 100 shops in October last year and opening another 33 in 2023.