The W–Cu composites with nanosized grain boundaries and high effective density were fabricated using a new fast isostatic hot pressing method. A significantly faster method was proposed for the formation of W–Cu composites in comparison to the traditional ones. The influence of both the high temperature and pressure conditions on the microstructure, structure, chemical composition, and density values were observed. It has been shown that W–Cu samples have a polycrystalline well-packed microstructure. The copper performs the function of a matrix that surrounds the tungsten grains. The W–Cu composites have mixed bcc-W (sp. gr. Im $\overline{3}$ m) and fcc-Cu (sp. gr. Fm $\overline{3}$ m) phases. The W crystallite sizes vary from 107 to 175 nm depending on the sintering conditions. The optimal sintering regimes of the W–Cu composites with the highest density value of 16.37 g/cm³ were determined. Tungsten–copper composites with thicknesses of 0.06–0.27 cm have been fabricated for the radiation protection efficiency investigation against gamma rays. It has been shown that W–Cu samples have a high shielding efficiency from gamma radiation in the 0.276–1.25 MeV range of energies, which makes them excellent candidates as materials for radiation protection.