The derivative of 1,2,4-thiadiazole (TDZ) can be considered as a perspective agent for the Alzheimer’s disease prevention. Due to a highly lipophilic character, the compound reveals good membrane permeability properties and poor solubility in aqueous media. In order to solve this problem, water-soluble biodegradable polymers: PEG 6000 (PEG), PVP K29-30 (PVP) and linear (A–B–A type) ethylene oxide-propylene oxide block copolymer Pluronic F127 (F127) were used in the present investigation to obtain binary and ternary TDZ composites (solid dispersions) with improved solubility and dissolution rate. Composites were prepared by a mechanical grinding procedure. Differential scanning calorimetry and FTIR spectroscopy were used to characterize the obtained samples. The interaction of TDZ with PVP after the grinding procedure was revealed. Shake-flask method was applied to measure the solubility of the composites. A dramatical increase in the solubility was shown for the solid dispersion with F127 above the critical micelle concentration. The dissolution behavior was studied with the help of the basket method at pH 1.2 and pH 6.8. The dissolution of TDZ/polymer solid dispersions was substantially accelerated as compared to pure TDZ and physical mixtures. The dissolution mechanism was estimated through the Korsmeyer–Peppas model equation. Franz diffusion cell and new Permeapad™ barrier were applied for the permeability assay. The permeability of TDZ in solid dispersions through the Permeapad™ barrier was shown to decrease in comparison with the pure TDZ. It was concluded that composites with PEG, PVP and F127 are an effective tool for increasing the solubility and dissolution of 1,2,4-thiadiazole derivative.