In this work, we developed quantitative structure–activity relationships (QSAR) models for prediction of oxygen radical absorbance capacity (ORAC) of flavonoids. Both linear (partial least squares—PLS) and non-linear models (artificial neural networks—ANNs) were built using parameters of two well-established antioxidant activity mechanisms, namely, the hydrogen atom transfer (HAT) mechanism defined with the minimum bond dissociation enthalpy, and the sequential proton-loss electron transfer (SPLET) mechanism defined with proton affinity and electron transfer enthalpy. Due to pronounced solvent effects within the ORAC assay, the hydration energy was also considered. The four-parameter PLS-QSAR model yielded relatively high root mean square errors (RMSECV = 0.783, RMSEE = 0.668, RMSEP = 0.900). Conversely, the ANN-QSAR model yielded considerably lower errors (RMSEE = 0.180 ± 0.059, RMSEP1 = 0.164 ± 0.128, and RMSEP2 = 0.151 ± 0.114) due to the inherent non-linear relationships between molecular structures of flavonoids and ORAC values. Five-fold cross-validation was found to be unsuitable for the internal validation of the ANN-QSAR model with a high RMSECV of 0.999 ± 0.253; which is due to limited sample size where resampling with replacement is a considerably better alternative. Chemical domains of applicability were defined for both models confirming their reliability and robustness. Based on the PLS coefficients and partial derivatives, both models were interpreted in terms of the HAT and SPLET mechanisms. Theoretical computations based on density functional theory at ωb97XD/6-311++G(d,p) level of theory were also carried out to further shed light on the plausible mechanism of anti-peroxy radical activity. Calculated energetics for simplified models (genistein and quercetin) with peroxyl radical derived from 2,2′-azobis (2-amidino-propane) dihydrochloride suggested that both SPLET and single electron transfer followed by proton loss (SETPL) mechanisms are competitive and more favorable than HAT in aqueous medium. The finding is in good accord with the ANN-based QSAR modelling results. Finally, the strongly predictive ANN-QSAR model was used to predict antioxidant activities for a series of 115 flavonoids designed combinatorially with flavone as a template. Structural trends were analyzed, and general guidelines for synthesis of new flavonoid derivatives with potentially potent antioxidant activities were given.