Development of efficient and green methods for extracting bioactive phytochemicals has great industrial value. Increasing environmental sensitivity at the global level has tremendously enhanced the demand for such methods. Azadirachta indica is a well-known medicinal tree. As glycerol has emerged as a green and safe extraction solvent for bioactive phytochemicals, this study aimed to investigate the efficacy of a glycerol–water solvent system to extract bioactive compounds from A. indica leaves. Modelling and optimisation were carried out by using response surface methodology (RSM) as per the Box–Behnken design with three variables, namely, solvent concentration, time and temperature. The responses were total phenolic content (TPC), total flavonoid content (TFC), 2,2-diphenyl-1-picrylhydrazyl (DPPH) radical scavenging activity and metal chelating activity (MCA). The optimum conditions found by numerical optimisation were a solvent concentration of 69.713%, a time period of 38.328 min and a temperature of 32.114 °C with the predicted values of TPC, TFC, %DPPH and %MCA as 5.27 mg gallic acid equivalents · g−1 DW (dry weight), 9.869 mg rutin equivalents · g−1 DW, 73.8% and 54.366%, respectively. The validation experiments showed almost the same results for each response with very low% errors (5.431–7.661). Increasing glycerol concentration in the extracting medium favoured the extraction of TPC, TFC and antioxidant phytochemicals, but for MCA, the trend was the opposite. In conclusion, 70% aqueous glycerol is an effective medium for the extraction of polyphenolic and antioxidant phytochemicals from A. indica leaves. Extraction models suggested by RSM have high prospects to be used on a large industrial scale.
