Lead-free (1-x)Bi0.5Na0.5TiO3-xBi(Mg0.5Ti0.5)O3 (BNT-BMT) (x=0.00-0.06) solid solutions were synthesized via a solid state processing technique, and the effects of BMT on the structural, microstructural, dielectric, ferroelectric, and piezoelectric properties were investigated. The XRD analysis demonstrated that BMT has no pronounced effect on the crystal structure of BNT in the composition range studied, where all samples consisted of a pure perovskite phase with rhombohedral symmetry. The temperature and frequency dependences of the dielectric constant revealed that the studied compositions exhibited dielectric diffuse-to-relaxor type phase transformation. The degree of deviation from the Curie-Weiss law increased with increasing BMT concentration. The addition of BMT significantly decreased the coercive field of BNT and resulted in enhanced remnant polarization and piezoelectric constant of 38 µC/cm2 and 108 pC/N, respectively at x=0.04. Polarization hysteresis was also measured at increased temperatures. These findings, along with the thermal hysteresis in the dielectric maximum, provide evidence for the observed diffuse-to-relaxor type phase transformation of these ceramics.