Supplemental dampers are an attractive mean to mitigate the response of dynamically excited structures. Typically, dampers are designed only after the main structure is completed, and they are added with the goal to increase structural damping and effectively reduce the dynamic response. Topology optimization offers the possibility of obtaining material layout distribution to meet the loading demands; however, most approaches only accommodate static deterministic loads, but dynamic responses are required to design damping systems and many of the most severe dynamic loads that civil structures withstand are stochastic in nature. Therefore, this paper proposes a reliability-based scheme to obtain simultaneously optimal topology and size/location of discrete dampers for stochastically excited structures. 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. An objective function of the optimization scheme is then defined as the first-passage probability, which is computed using the stationary covariances. The proposed topology optimization scheme is illustrated for a mid-rise building subjected to stochastic ground motion excitation. The results presented herein demonstrate the efficacy of the proposed approach for efficient simultaneous optimization of topology and damping distribution of stochastically excited structures.