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After a seismic event, tsunami early warning systems (TEWSs) try to accurately forecast the maximum height of incident waves at specific target points in front of the coast. The goal is to launch early warnings on locations where the impact of tsunami waves can be destructive, and to refine these forecasts in urgent computing mode in its immediate aftermath, to help organizing potential recovery operations. For improving the accuracy and computational efficiency of classic tsunami forecasting methods based on simulation models, scientists have recently started to exploit machine learning techniques to process pre-computed simulation data, in order to extract tsunami predictive models. However, the proposed approaches, mainly based on neural networks, suffer of high training time and limited model explainability. This paper describes a machine learning approach based on regression trees to model and forecast tsunami evolutions to overtake these issues. The experimental evaluation, performed on a real-world earthquake and tsunami simulation case study, shows that regression trees achieve high forecasting accuracy. Moreover, they provide domain experts with fully-explainable and interpretable models, which are a valuable support for environmental scientists because they describe underlying rules and patterns behind the models and allow for an explicit inspection of their functioning.