The (1−x)BaTiO3–xBaSnO3 (0⩽x⩽0.30) perovskite solid solution ceramics were prepared by solid state reaction and studied by dielectric spectroscopy. The complex dielectric permittivity was measured as a function of frequency (0.1Hz–100kHz) in the temperature (T) range of 123–573K. The transition from the high-temperature paraelectric state where the dielectric constant obeys the Curie-Weiss law to the ergodic cluster state is found to occur at the same temperature of 485K in all the compositions of x⩾0.04 and at lower temperatures in those with a smaller x. For 0⩽x⩽xc=0.19, the temperature of the dielectric peak Tm, corresponding to the diffuse transition from the ergodic polar cluster state to the ferroelectric state, decreases with increasing x and does not depend on frequency. The diffuseness of the peak gradually increases. For x>xc, the permittivity exhibits relaxor behavior with the frequency-dependent Tm satisfying the Vogel-Fulcher law. The temperature variation of the permittivity on the high-temperature slope of the peak (T>Tm) is characterized by the characteristic Lorenz-type quadratic law for relaxors, with the diffuseness increasing with the increase of x. The mechanisms of the dielectric response in different parts of the phase diagram are discussed. In particular, the crossover from diffuse ferroelectric phase transition to relaxor ferroelectric behavior is attributed to the appearance at x>xc of the additional dielectric contribution arising from the flipping of the local polarization of the polar clusters. The temperature-composition phase diagram of the Ba(Ti1−xSnx)O3 system has been established, which delimits the paraelectric, ergodic polar cluster, nonergodic ferroelectric, and relaxor phases (states) and indicates the crossover from ferroelectric to relaxor behavior at x=xc.