Supplemental damping devices present an attractive means to improve the structural system. Typically, dampers are designed after the structural system is selected, and they are added to increase structural damping and effectively reduce the dynamic response. On the other hand, topology optimization offers a possibility to obtain an efficient structural system but not the damper placement. Therefore, this study proposes a framework to obtain simultaneously optimal topology as well as the size and spatial distribution of discrete supplemental viscous damping devices for stochastically-excited buildings. The excitation is modeled as a stationary zero-mean filtered white noise, the excitation model is combined with the structural model to form an augmented representation, and the stationary covariances of the structural responses of interest are obtained by solving a Lyapunov equation. The objective function is defined in terms of the stationary covariance. A gradient-based method is used to update the design variables, and the sensitivities are computed using an adjoint method requiring the solution of an additional Lyapunov equation. The proposed topology optimization scheme is illustrated to obtain the optimal lateral resisting system together with the discrete dampers distribution for buildings subjected to stochastic ground motion. The results presented herein demonstrate the efficiency of the proposed approach to perform simultaneous optimization of topology and damper distribution of stochastically excited structures.