We propose a holistic framework based on state-of-the-art methods in Machine Learning and Optimization to prescribe influenza vaccine composition that are specific to a region, or a country based on historical data concerning the rates of circulation of predominant viruses. First, we develop a tensor completion formulation to predict rates of circulation of viruses for the next season based on historical data. Then, taking into account the uncertainty in the predicted rates of circulation of predominant viruses, we propose a novel robust prescriptive framework for selecting suitable strains for each subtypes of the flu virus: Influenza A (H1N1 and H3N2) and B viruses for production. Finally, we train optimal regression trees to predict efficacy of the prescribed vaccine in terms of both morbidity and mortality rates using a set of weighted distances between the vaccine-strain and the actual circulating viruses during a flu season for each subtypes of the flu virus. Through numerical experiments, we show that our proposed vaccine compositions could potentially lower morbidity by 11-14% and mortality by 8-11% over vaccine compositions proposed by World Health Organization (WHO) for Northern hemisphere, and lower morbidity by 8-10% and mortality by 6-9% over vaccine compositions proposed by U.S Food and Drug Administration (FDA) for USA, and finally, lower morbidity by 10-12\% and mortality by 9-11% over vaccine compositions proposed by European Medicines Agency (EMA) for Europe.