Physicochemical and microbiological changes in yogurts determine their storage and shelf life. Thus, monitoring yogurt quality is essential for consumer acceptance and food safety. However, traditional techniques of yogurt quality analysis are food-destructive, environment polluting, costly, and time-consuming. On the other hand, nondestructive techniques only measure a single quality property, not expressing the yogurt overall quality. In this study, predictive models validated by bootstrapping and cross-validation methods demonstrate the biogenic amine index (BAI) as a nondestructive monitoring system of overall quality during storage. The optical parameter was a strong nondestructive predictor of the BAI for both cow’s milk yogurt, CY (Rv = 0.944; p = 0.007), and goat’s milk yogurt, GY (Rv = 0.909; p = 0.009). For CY, the reduction in the overall acceptability during storage was a strong predictor of the BA index (Rv = 0.869; p < 0.05), with a suitable prediction accuracy in the application set of commercial samples (Rapplic = 0.847; accuracy = 84.06%;). For GY, the model had a low prediction capability of the overall quality. Given the high predictive ability of the model, the BAI has a great potential to perform a nondestructive assessment of the overall quality of CY during storage.