Curcumin possesses various effective medicinal properties, such as anti-cancer, anti-Alzheimer's, anti-inflammatory, and antioxidant effects, where its free radical scavenging activities play a crucial role in its therapeutic mechanisms. Although the antioxidant properties of curcumin and its derivatives have been previously studied, a systematic investigation of the thermodynamics and kinetics of the reaction with the hydroperoxide radical (HOO˙) – a standardized free radical – in different solvents is lacking. This study examined the HOO˙ radical scavenging activities of two curcumin derivatives, specifically curcumin I (Cur-I) and curcumin III (Cur-III), in water and pentyl ethanoate (PEA) solutions using Density Functional Theory (DFT) approaches. The antioxidant properties of the neutral and anionic forms of their tautomers, including the keto–enol and diketone forms, were explored via three standard mechanisms: hydrogen abstraction (Abs), radical addition (Add), and single electron transfer (SET). Intrinsic parameters, thermochemical parameters, and kinetics of the curcumin-HOO˙ reactions were systematically characterized. As a result, the overall rate constant for the reaction of Cur-I in the water (9.36 × 107 M−1 s−1) is approximately 3.6 times higher than that of Cur-III (2.60 × 107 M−1 s−1). Meanwhile, the rate constants in PEA solvent are less significant, being 4.02 × 101 M−1 s−1 and 8.16 × 102 M−1 s−1 for Cur-I and Cur-III, respectively. Due to the dominant molar fraction of the keto–enol form compared to the diketone, the reaction rates are primarily attributed to the keto–enol form. The SET reaction of dianionic form contributes a decisive proportion to the overall rate constants of both Cur-I and Cur-III. Finally, an analysis of the chemical nature of the Abs reactions reveals that the most predominant hydrogen transfer at the phenolic –OH groups (i.e., O22H and O23H) occurs via a proton-coupled electron transfer (PCET) mechanism.