Coronavirus Disease 2019 (COVID-19) demonstrated the need for accurate and fast diagnosis methods for emergent viral diseases. Soon after the emergence of COVID-19, medical practitioners used X-ray and computed tomography (CT) images of patients' lungs to detect COVID-19. Machine learning methods are capable of improving the identification accuracy of COVID-19 in X-ray and CT images, delivering near real-time results, while alleviating the burden on medical practitioners. In this work, we demonstrate the efficacy of a support vector machine (SVM) classifier, trained with a combination of deep convolutional and handcrafted features extracted from X-ray chest scans. We use this combination of features to discriminate between healthy, common pneumonia, and COVID-19 patients. The performance of the combined feature approach is compared with a standard convolutional neural network (CNN) and the SVM trained with handcrafted features. We find that combining the features in our novel framework improves the performance of the classification task compared to the independent application of convolutional and handcrafted features. Specifically, we achieve an accuracy of 0.988 in the classification task with our combined approach compared to 0.963 and 0.983 accuracy for the handcrafted features with SVM and CNN respectively.