This study examines the ability of damping devices placed between outrigger trusses and perimeter columns to mitigate dynamic vibrations in a tall building structure. The implementation of this approach to mitigate wind-induced vibrations for a 40-story building is assessed via a series of real-time hybrid simulations (RTHS), in which a numerical model of the complete building actively interfaces with physical dampers in the laboratory via actuators. In a RTHS, the overall structure is divided into analytical and experimental substructures, where the latter is challenging to model numerically and therefore evaluated in the laboratory as the experimental substructure. The experimental substructure for the RTHS in this study includes two full-scale nonlinear viscous dampers, and the rest of the building is modelled numerically as the analytical substructure. The coupling between the experimental and the analytical substructures is achieved in real time by enforcing compatibility and equilibrium between the two substructures during a simulation. Results of the RTHS show the feasibility of reducing the root mean square (RMS) and maximum wind-induced roof accelerations by up to 43% and 37%, respectively, when the building is subjected to a 700-year mean recurrence interval (MRI) storm with a 177 km/h basic wind speed. The stiffness of the members in the damper force path and the number of dampers play a major rule in controlling the wind induced vibrations. The results show that the as-built outrigger truss and column members require additional stiffening in order to maximize the benefit of adding the dampers to the building. There is a limit to the number of dampers that can be used beyond which minimal benefit is gained towards improving the performance of the building. RTHS are also used to estimate the equivalent viscous damping of the building with the outrigger damping system, which is found to be 8.7% of critical damping for the 1st mode of vibration.