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Our research aims to improve the accuracy of Earthquake Early Warning (EEW) systems by means of machine learning. EEW systems are designed to detect and characterize medium and large earthquakes before their damaging effects reach a certain location. Traditional EEW methods based on seismometers fail to accurately identify large earthquakes due to their sensitivity to the ground motion velocity. The recently introduced high-precision GPS stations, on the other hand, are ineffective to identify medium earthquakes due to its propensity to produce noisy data. In addition, GPS stations and seismometers may be deployed in large numbers across different locations and may produce a significant volume of data consequently, affecting the response time and the robustness of EEW systems.In practice, EEW can be seen as a typical classification problem in the machine learning field: multi-sensor data are given in input, and earthquake severity is the classification result. In this paper, we introduce the Distributed Multi-Sensor Earthquake Early Warning (DMSEEW) system, a novel machine learning-based approach that combines data from both types of sensors (GPS stations and seismometers) to detect medium and large earthquakes. DMSEEW is based on a new stacking ensemble method which has been evaluated on a real-world dataset validated with geoscientists. The system builds on a geographically distributed infrastructure, ensuring an efficient computation in terms of response time and robustness to partial infrastructure failures. Our experiments show that DMSEEW is more accurate than the traditional seismometer-only approach and the combined-sensors (GPS and seismometers) approach that adopts the rule of relative strength.