The article presents the results of a study of the effect of the content of styrene-butadiene elastomer on the change in ultimate tensile stress, tensile yield strength, elongation at break, flexural strength, enthalpy and melting temperature, Vicat softening temperature, and melt flow rate of polymer blends based on a wide range of thermoplastic polyolefins: high-density polyethylene, low-density polyethylene, polypropylene, ethylene-hexene-1 copolymer, polypropylene random copolymer, and block copolymer of ethylene with propylene. Nanoparticles of technical carbon (TC), aluminum, and calcium stearate were used as fillers. It has been shown that, depending on the type of polyolefin used and the specific concentration of elastomer, the polymer mixture can acquire the properties of a thermoplastic elastomer (TPE). In high-density polyethylene and an ethylene-hexene-1 copolymer, the properties of TPE appear at an elastomer concentration of 30 wt %; in low-density polyethylene, this effect occurs at its 20 wt % content. In polypropylene, polypropylene random copolymer, and ethylene-propylene block copolymer, TPE properties appear at 40 wt % concentration of the elastomeric component. This was confirmed by the results of scanning electron microscopy, X-ray diffraction analysis, differential scanning calorimetry, as well as the “stress–strain” dependence of polymer mixtures. To achieve technological compatibility and miscibility of non-polar polyolefins with polar elastomer, compatibilizers based on high-density polyethylene and polypropylene modified with maleic anhydride were used. It is shown that the equality of the values of the ultimate tensile stress and the tensile yield strength is a consequence of the occurrence of phase inversion in the polymer mixture, that is, change of the dispersed medium to the dispersed phase and vice versa.