Nightclub entrepreneur Sina Moradian and builder William Palmer paid £114,000 for the former Whitehorse pub in the Ropewalks area of the city. The price was £34,000 over the guide.
The building was painted with a Banksy depicting a giant rat with a marker pen and red zig-zag doodles, as a commission for an art festival in 2004.
The building is Grade II-listed and any attempt to remove the artwork would have to be approved by the cityís planning committee.
The new owners intend to turn the ground floor of the building into an off-licence with student accommodation above.
Palmer said: ďI donít know a lot about art. We have had our eyes on the building for a while because of its prominent location but have been waiting for it to become available at the right price. Ideally we would like to retain the artwork but the renovation works take priority.Ē