Highly optical transparent tellurite glasses are attractive and viable as alternative materials for absorbing gamma-ray photons in the design of radiation protection structures. This report examines the potential of new tellurite glass systems (TeO2-ZnO-WO3-Bi2O3) doped with Er3+ (TZWB-Er), Tm3+ (TZWB-Tm), and Nd3+ (TZWB-Nd) as shielding materials against charged and uncharged radiation. The mass attenuation coefficient, μ/ρ of the glasses was computed by XCOM software and data from simulations of photon transmission in the PHIT code. The total stopping powers and range of beta particles β, H+, He2+, and C6+ in the glasses were estimated by ESTAR, PSTAR, ASTAR, and SRIM software at particle kinetic energies within 0.1–10 MeV. The fast neutron (FN) removal and thermal neutron absorption cross-sections in the glasses were also computed. The stopping powers and ranges of the considered charged particles showed variations that depended on the kinetic energy of the particles and chemical composition of the glasses. The TZWB-M glasses are better alternatives as gamma-radiation shields compared to traditional shielding substances such as concrete, some commercial glass shields, and recently recommended glass shields. The glasses are thus recommended for the design of radiation safety structures.