The solubility and thermodynamic analysis of baricitinib (BNB) in various dimethyl sulfoxide (DMSO) + water mixtures were performed. The “mole fraction solubilities (xe)” of BNB in DMSO and water mixtures were determined at “T = 298.2–323.2 K” and “p = 0.1 MPa” using an isothermal saturation technique. “Hansen solubility parameters (HSPs)” of BNB, pure DMSO, pure water and “DMSO + water” mixtures free of BNB were also estimated. The xe data of BNB was regressed well by five different thermodynamics-based co-solvency models, which included “Apelblat, Van’t Hoff, Yalkowsky-Roseman, Jouyban-Acree and Jouyban-Acree-Van’t Hoff models” with overall deviations of <5.0%. The highest and lowest xe value of BNB was computed in pure DMSO (1.69 × 10−1 at T = 323.2 K) and pure water (2.23 × 10−5 at T = 298.2 K), respectively. The HSP of BNB was found to be closer to that of pure DMSO. Based on activity coefficient data, maximum solute–solvent molecular interactions were observed in BNB-DMSO compared to BNB-water. The results of “apparent thermodynamic analysis” indicated endothermic and entropy-drive dissolution of BNB in all “DMSO + water” combinations including mono-solvents (water and DMSO). “Enthalpy-entropy compensation analysis” showed enthalpy-driven to be the main mechanism of solvation of BNB.