Recent advances in the e-commerce fashion industry have led to an exploration of novel ways to enhance buyer experience via improved personalization. Predicting a proper size for an item to recommend is an important personalization challenge, and is being studied in this work. Earlier works in this field either focused on modeling explicit buyer fitment feedback or modeling of only a single aspect of the problem (e.g., specific category, brand, etc.). More recent works proposed richer models, either content-based or sequence-based, better accounting for content-based aspects of the problem or better modeling the buyers online journey. However, both these approaches fail in certain scenarios: either when encountering unseen items (sequence-based models) or when encountering new users (content-based models). To address the aforementioned gaps, we propose PreSizE - a novel deep learning framework which utilizes Transformers for accurate size prediction. PreSizE models the effect of both content-based attributes, such as brand and category, and the buyers purchase history on her size preferences. Using an extensive set of experiments on a large-scale e-commerce dataset, we demonstrate that PreSizE is capable of achieving superior prediction performance compared to previous state-of-the-art baselines. By encoding item attributes, PreSizE better handles cold-start cases with unseen items, and cases where buyers have little past purchase data. As a proof of concept, we demonstrate that size predictions made by PreSizE can be effectively integrated into an existing production recommender system yielding very effective features and significantly improving recommendations.