The office tower faces the Treasury Building on Queen Street, which formerly housed the Treasury Casino, and the former Law Courts Complex on Adelaide Street.
The site is now home to the Brisbane Quarter mixed-use hotel, office and residential development.
Brisbane Square is owned by ABN AMRO and was designed by international architects Denton Corker Marshall.
The original development application included a number of residential floors on the top of the building, however, this was rejected on the basis that noise levels would be excessive.
The site of Brisbane Square was previously occupied by the now-demolished Prudential Building, state headquarters of the British insurance company Prudential Assurance Co.