This study outlines findings from an investigation into the development of a hydrometallurgical process for manufacturing various forms of zinc perrhenate, entirely from waste from recycling and from the Zn–Pb industry. Scraps of Re-bearing Ni-based superalloys and acidic waste, circulating zinc solutions generated during the production of Zn by the electrolytic method and which contain >45 g/dm3 of Zn, Na, Mn, and Mg, were used in the research. In the publication, the conditions for the production of three types of zinc perrhenate, i.e., Zn(ReO4)2·4H2O, Zn(ReO4)2, and Zn(ReO4)2·2H2O, are presented. As a result of the analysis of the obtained results, it was concluded that to obtain the above-mentioned forms of zinc perrhenate, zinc carbonate can be used, precipitated from acidic, waste, and multi-component solutions after their prior neutralization to pH 4.0 and partial purification from Mn, Mg, and Na using metallurgical zinc oxide. Zinc carbonate should be precipitated using Na2CO3 at pH 6.3 and subsequently purified from other impurities, i.e., Mg, Na, and Mn, using aqueous ammonia solutions. As a result, zinc carbonate was obtained, which was used in a reaction with an aqueous solution of HReO4 to produce zinc perrhenate. The precipitated forms of Zn(ReO4)2 were obtained by appropriately drying the crude and hydrated Zn(ReO4)2 to obtain its tetrahydrate, dihydrate, and anhydrous forms, respectively, using drying temperatures of 55, 135, and 185 °C. The developed technology has been submitted for a patent and is an example of a technology founded on the principles of sustainable development, with a particular emphasis on the minimalization of loss of rhenium and zinc at all stages of its realization.