A new structural system conceived to control Base Isolated System vibrations under random excitations is analyzed. The new system combines the Tuned Mass Damping strategy with the Isolation concept in order to obtain a new system which principally attenuates the effects of the seismic excitation components with frequencies close to the fundamental natural vibration one. The Random response of equivalent linear Base Isolated Systems controlled by Tuned Mass Dampers subject to horizontal random excitations is analyzed. Considering the superstructure motion described by its first modal contribution, a three‐degree‐of‐freedom linear model subject to stationary Gaussian excitations, modelled by the modified Kanai‐Tajimi power density spectrum, was used in this analysis. The standard deviation response ratio of the new system respect to the one of the base isolated system was evaluated based on a wide range of parameters. Optimal parameters which minimize structural response were also obtained.