The incumbent, The Brooklyn Brothers, did not take part in the pitch. The agency parted company with the bookmaker in March, just three months after being appointed to the business.
The Bank will take responsibility for producing William Hill's advertising activity, including a brief to promote its association with football.
Launching in the run-up to the World Cup, The Bank will create a campaign that aims to promote William Hill as the "home of betting" and will include TV, outdoor, print and online channels, as well as promotional and radio activity.
The Bank's appointment marks a shift in marketing strategy for the bookmaker, instigated by its new group brand and marketing director, Kristof Fahy.