The Electrocardiogram (ECG) is a clinical tool for identifying cardiovascular diseases (CVDs), including arrhythmias. The manual evaluation of ECG signals poses significant challenges due to subtle physiological variations in both normal and pathological conditions, especially in high volume cardiac cases. To address this, automated classification of ECG signals has emerged as an essential aid for healthcare professionals, ensuring accurate and efficient analysis. Existing approaches predominantly utilize convolutional neural networks (CNNs) for feature extraction; however, these methods often struggle to fully capture long-term dependencies and intricate pathological distinctions. Transformer networks (TransNets), recognized for their effectiveness in modeling sequence data, complement CNNs by capturing long-range temporal correlations, but their reliance on extensive datasets can make them computationally complex. This study introduces a hybrid model integrating CNN and Transformer networks for arrhythmia classification. The TransNet-based CNN model was evaluated on the MIT-BIH Arrhythmia Database (MIT-ArrhyDB) to classify ECG signals into five distinct arrhythmia categories based on morphological features. The hybrid model achieved an overall accuracy of 98.95% and an F1-Score of 98.52%, outperforming existing state-of-the-art techniques. Experimental results underscore the efficacy of combining CNNs and Transformer networks, showcasing their potential for enhanced ECG signal analysis in clinical applications.