COVID-19 which was announced as a pandemic on 11 March 2020, is still infecting millions to date as the vaccines that have been developed do not prevent the disease but rather reduce the severity of the symptoms. Until a vaccine is developed that can prevent COVID-19 infection, the testing of individuals will be a continuous process. Medical personnel monitor and treat all health conditions; hence, the time-consuming process to monitor and test all individuals for COVID-19 becomes an impossible task, especially as COVID-19 shares similar symptoms with the common cold and pneumonia. Some off-the-counter tests have been developed and sold, but they are unreliable and add an additional burden because false-positive cases have to visit hospitals and perform specialized diagnostic tests to confirm the diagnosis. Therefore, the need for systems that can automatically detect and diagnose COVID-19 automatically without human intervention is still an urgent priority and will remain so because the same technology can be used for future pandemics and other health conditions. In this paper, we propose a modified machine learning (ML) process that integrates deep learning (DL) algorithms for feature extraction and well-known classifiers that can accurately detect and diagnose COVID-19 from chest CT scans. Publicly available datasets were made available by the China Consortium for Chest CT Image Investigation (CC-CCII). The highest average accuracy obtained was 99.9% using the modified ML process when 2000 features were extracted using GoogleNet and ResNet18 and using the support vector machine (SVM) classifier. The results obtained using the modified ML process were higher when compared to similar methods reported in the extant literature using the same datasets or different datasets of similar size; thus, this study is considered of added value to the current body of knowledge. Further research in this field is required to develop methods that can be applied in hospitals and can better equip mankind to be prepared for any future pandemics.