Promotions and discounts are essential components of modern e-commerce platforms, where they are often used to incentivize customers towards purchase completion. Promotions also affect revenue and may incur a monetary loss that is often limited by a dedicated promotional budget. We study the Online Constrained Multiple-Choice Promotions Personalization Problem, where the optimization goal is to select for each customer which promotion to present in order to maximize purchase completions, while also complying with global budget limitations. Our work formalizes the problem as an Online Multiple Choice Knapsack Problem and extends the existent literature by addressing cases with negative weights and values. We provide a real-time adaptive method that guarantees budget constraints compliance and achieves above 99.7% of the optimal promotional impact on various datasets. Our method is evaluated on a large-scale experimental study at one of the leading online travel platforms in the world.