This paper proposes an integrated damping system that aims at providing relatively high damping levels through the mobilization of a proportion of the structure's own mass. This offers significantly higher mass levels and, consequently, considerably more damping compared to conventional tuned mass dampers. Fluid viscous dampers are used to control accelerations in parallel with springs to resist the static loads applied to the moving mass. The advantages of employing relatively large mass levels in achieving considerable damping and reducing sensitivity to tuning are first analyzed using an idealized two degree of freedom structural representation. This is then followed by a description of the proposed “integrated damping system,” which is illustrated through a case study of a 250‐m tall building. The benefits of the proposed damping system are demonstrated through several numerical parametric assessments, as well as a selected suite of earthquake records. For the adopted case study, it is shown that, besides reducing the level of perceivable accelerations, the use of the suggested arrangement can offer an equivalent damping exceeding 50% of the critical damping, resulting in more than 40% reduction in the wind loads as well as over 60% reduction in displacement and acceleration response under seismic excitations.