The aging population has led to a growing number of falls in our society, affecting global public health worldwide. This paper presents CareFall, an automatic Fall Detection System (FDS) based on wearable devices and Artificial Intelligence (AI) methods. CareFall considers the accelerometer and gyroscope time signals extracted from a smartwatch. Two different approaches are used for feature extraction and classification: i) threshold-based, and ii) machine learning-based. Experimental results on two public databases show that the machine learning-based approach, which combines accelerometer and gyroscope information, outperforms the threshold-based approach in terms of accuracy, sensitivity, and specificity. This research contributes to the design of smart and user-friendly solutions to mitigate the negative consequences of falls among older people.