The current study investigates the dissolution rate performance of amorphous solid solutions of a poorly water-soluble drug, efavirenz (EFV), in amorphous Soluplus® (SOL) and Kollidon® VA 64 (KVA64) polymeric systems. For the purpose of the study, various formulations with varying drug loadings of 30, 50, and 70% w/w were developed via hot-melt extrusion processing and adopting a Box-Behnken design of experiment (DoE) approach. The polymers were selected based on the Hansen solubility parameter calculation and the prediction of the possible drug-polymer miscibility. In DoE experiments, a Box-Behnken factorial design was conducted to evaluate the effect of independent variables such as Soluplus® ratio (A), HME screw speed (A), and processing temperature (A), and Kollidon®VA64 ratio (B), screw speed (B), and processing temperature (B) on responses such as solubility (X and Y) and dissolution rate (X and Y) for both ASS [EFV:SOL] and BSS [EFV:KVA64] systems. DSC and XRD data confirmed that bulk crystalline EFV transformed to amorphous form during the HME processing. Advanced chemical analyses conducted via 2D COSY NMR, FTIR chemical imaging, AFM analysis, and FTIR showed that EFV was homogenously dispersed in the respective polymer matrices. The maximum solubility and dissolution rate was observed in formulations containing 30% EFV with both SOL and KVA64 alone. This could be attributed to the maximum drug-polymer miscibility in the optimized formulations. The actual and predicted values of both responses were found precise and close to each other.