The problem of flight delay prediction is approached most often by predicting a delay class or value. However, the aviation industry can benefit greatly from probabilistic delay predictions on an individual flight basis, as these give insight into the uncertainty of the delay predictions. Therefore, in this study, two probabilistic forecasting algorithms, Mixture Density Networks and Random Forest regression, are applied to predict flight delays at a European airport. The algorithms estimate well the distribution of arrival and departure flight delays with a Mean Absolute Error of less than 15 min. To illustrate the utility of the estimated delay distributions, we integrate these probabilistic predictions into a probabilistic flight-to-gate assignment problem. The objective of this problem is to increase the robustness of flight-to-gate assignments. Considering probabilistic delay predictions, our proposed flight-to-gate assignment model reduces the number of conflicted aircraft by up to 74% when compared to a deterministic flight-to-gate assignment model. In general, the results illustrate the utility of considering probabilistic forecasting for robust airport operations’ optimization.