Gears are reliable and robust elements that are found in any power transmission system. However, gears are prone to present incipient faults, such as wear, since they are constantly subjected to contact forces. Due to gears playing a key role in many industrial processes, it is important to develop condition monitoring strategies that ensure the proper functioning of the related power transmission system and the overall components. In this regard, the data on entropy provide relevant information that allow us to identify and quantify the effect of different wear levels in gears. Therefore, in this work, we proposed the use of seven entropy-related features to perform the identification of different wear severities in a gearbox. The novelty of this proposal lies in the use of the entropy features to carry out a high-performance characterization of the available vibration signals that are acquired from experimental tests. The novelty of this proposal lies in the fusion of three different techniques: entropy features, linear discriminant analysis, and artificial neural networks to obtain a machine learning approach for improving the detection of different wear severities in gears compared to other reported methodologies. This situation is achieved due to the high-performance characterization of the available vibration signals that are acquired from experimental tests. Additionally, the entropy features are subjected to a feature space transformation by means of linear discriminant analysis to obtain a 2D representation and, finally, the set of features extracted by linear discriminant analysis are used as inputs of a neural network-based classifier to determine the severity of wear that is present in the gears. The proposed methodology is validated and compared with a conventional statistical approach to show the improvement in the classification.