Human life necessitates high-quality sleep. However, humans suffer from a lower quality of life because of sleep disorders. The identification of sleep stages is necessary to predict the quality of sleep. Manual sleep-stage scoring is frequently conducted through sleep experts’ visually evaluations of a patient’s neurophysiological data, gathered in sleep laboratories. Manually scoring sleep is a tough, time-intensive, tiresome, and highly subjective activity. Hence, the need of creating automatic sleep-stage classification has risen due to the limitations imposed by manual sleep-stage scoring methods. In this study, a novel machine learning model is developed using dual-channel unipolar electroencephalogram (EEG), chin electromyogram (EMG), and dual-channel electrooculgram (EOG) signals. Using an optimum orthogonal filter bank, sub-bands are obtained by decomposing 30 s epochs of signals. Tsallis entropies are then calculated from the coefficients of these sub-bands. Then, these features are fed an ensemble bagged tree (EBT) classifier for automated sleep classification. We developed our automated sleep classification model using the Sleep Heart Health Study (SHHS) database, which contains two parts, SHHS-1 and SHHS-2, containing more than 8455 subjects with more than 75,000 h of recordings. The proposed model separated three classes if sleep: rapid eye movement (REM), non-REM, and wake, with a classification accuracy of 90.70% and 91.80% using the SHHS-1 and SHHS-2 datasets, respectively. For the five-class problem, the model produces a classification accuracy of 84.3% and 86.3%, corresponding to the SHHS-1 and SHHS-2 databases, respectively, to classify wake, N1, N2, N3, and REM sleep stages. The model acquired Cohen’s kappa () coefficients as 0.838 with SHHS-1 and 0.86 with SHHS-2 for the three-class classification problem. Similarly, the model achieved Cohen’s of 0.7746 for SHHS-1 and 0.8007 for SHHS-2 in five-class classification tasks. The model proposed in this study has achieved better performance than the best existing methods. Moreover, the model that has been proposed has been developed to classify sleep stages for both good sleepers as well as patients suffering from sleep disorders. Thus, the proposed wavelet Tsallis entropy-based model is robust and accurate and may help clinicians to comprehend and interpret sleep stages efficiently.