The possibility of improving the properties of porous geopolymer materials based on ash and slag waste from thermal power plants by adjusting their chemical composition is considered. An X-ray phase analysis of ash and slag wastes was carried out, the geopolymers’ precursor compositions were calculated, and additives to correct their chemical composition were selected. The samples were synthesized and their physical and mechanical properties (density, porosity, compressive strength, thermal conductivity) were analyzed. The micro- and macro-structure of the samples and the pore distribution of the obtained geopolymers were studied and pore-distribution histograms were obtained. The influence of Si:Al ratio on structural changes was described. The geopolymers’ phase composition was studied, consisting of an amorphous phase and high quartz and mullite. A conclusion about the applicability of this method for obtaining high-quality porous geopolymers was made.