Stevia rebaudiana (Bertoni) leaves consist of dietetically important diterpene steviol glycosides (SGs): stevioside (ST) and rebaudioside-A (Reb-A). ST and Reb-A are key sweetening compounds exhibiting a sweetening potential of 100 to 300 times more intense than that of table sucrose. Ultrasound-assisted extraction (UAE) of SGs was optimized by effective process optimization techniques, such as response surface methodology (RSM) and artificial neural network (ANN) modeling coupled with genetic algorithm (GA) as a function of ethanol concentration (X1: 0–100%), sonication time (X2: 10–54 min), and leaf–solvent ratio (X3: 0.148–0.313 g·mL−1). The maximum target responses were obtained at optimum UAE conditions of 75% (X1), 43 min (X2), and 0.28 g·mL−1 (X3). ANN-GA as a potential alternative indicated superiority to RSM. UAE as a green technology proved superior to conventional maceration extraction (CME) with reduced resource consumption. Moreover, UAE resulted in a higher total extract yield (TEY) and SGs including Reb-A and ST yields as compared to those that were obtained by CME with a marked reduction in resource consumption and CO2 emission. The findings of the present study evidenced the significance of UAE as an ecofriendly extraction method for extracting SGs, and UAE scale-up could be employed for effectiveness on an industrial scale. These findings evidenced that the UAE is a high-efficiency extraction method with an improved statistical approach.