Between 293.2 and 313.2 K and at 0.1 MPa, the solubility of the weak base, cinnarizine (CNZ) (3), in various {Transcutol-P (TP) (1) + water (2)} combinations is reported. The Hansen solubility parameters (HSP) of CNZ and various {(TP) (1) + water (2)} mixtures free of CNZ were also predicted using HSPiP software. Five distinct cosolvency-based mathematical models were used to link the experimentally determined solubility data of CNZ. The solubility of CNZ in mole fraction was increased with elevated temperature and TP mass fraction in {(TP) (1) + water (2)} combinations. The maximum solubility of CNZ in mole fraction was achieved in neat TP (5.83 × 10−2 at 313.2 K) followed by the minimum in neat water (3.91 × 10−8 at 293.2 K). The values of mean percent deviation (MPD) were estimated as 2.27%, 5.15%, 27.76%, 1.24% and 1.52% for the “Apelblat, van’t Hoff, Yalkowsky–Roseman, Jouyban–Acree, and Jouyban–Acree–van’t Hoff models”, respectively, indicating good correlations. The HSP value of CNZ was closed with that of neat TP, suggesting the maximum solubilization of CNZ in TP compared with neat water and other aqueous mixtures of TP and water. The outcomes of the apparent thermodynamic analysis revealed that CNZ dissolution was endothermic and entropy-driven in all of the {(TP) (1) + water (2)} systems investigated. For {(TP) (1) + water (2)} mixtures, the enthalpy-driven mechanism was determined to be the driven mechanism for CNZ solvation. TP has great potential for solubilizing the weak base, CNZ, in water, as demonstrated by these results.