Vibration signals captured with an accelerometer carry essential information about Rolling Element Bearings (REBs) faults in rotating machinery, and the envelope spectrum has proven to be a robust tool for their diagnosis at an early stage of development. In this paper, Cepstrum Pre-Whitening (CPW) has been applied to REBs’ signals to enhance and extract health-state condition indicators from the preprocessed signals’ envelope spectra. These features are used to train some of the state-of-the-art Machine Learning (ML) algorithms, combined with time-domain features such as basic statistics, high-order statistics and impulsive metrics. Before training, these features were ranked according to statistical techniques such as one-way ANOVA and the Kruskal–Wallis test. A Convolutional Neural Network (CNN) has been designed to implement the classification of REBs’ signals from a Deep Learning (DL) point of view, receiving raw time signals’ greyscale images as inputs. The different ML models have yielded validation accuracies of up to 87.6%, while the CNN yielded accuracy of up to 77.61%, for the entire dataset. In addition, the same models have yielded validation accuracies of up to 97.8%, while the CNN, 90.67%, where signals from REBs with faulty balls have been removed from the dataset, highlighting the difficulty of classifying such faults. Furthermore, from the results of the different ML algorithms compared to those of the CNN, frequency-domain features have proven to be highly relevant condition indicators combined with some time-domain features. These models can be potentially helpful in applications that require early diagnosis of REBs faults, such as wind turbines, vehicle transmissions and industrial machinery.