The COVID-19 pandemic has caused millions of deaths and changed daily life globally. Countries have declared a half or full lockdown to prevent the spread of COVID-19. According to medical doctors, as many people as possible should be tested to identify their status, and corresponding actions then should be taken for COVID-19 positive cases. Despite the clear necessity of these medical tests, many countries are still struggling to acquire them. This fact clearly indicates the necessity of a large-scale, cheap, fast, and accurate alternative pre-screening tool that can be used for the diagnosis of COVID-19 while waiting for the medical tests. To this end, a novel end-to-end transfer learning-based deep learning approach that uses only a given cough sound for the diagnosis of COVID-19 was proposed in this study.The proposed models employed various pre-trained deep neural networks, namely, VGG19, ResNet50V2, DenseNet121, and MobileNet, via the transfer-learning technique. Then, these models were evaluated on a gold standard dataset, namely, Cambridge Data. According to the experimental result, the proposed model, which employed the MobileNet via the transfer-learning technique, provided the best accuracy, 86.42 %, and outperformed the state-of-the-art. Thus, the proposed model has the potential to provide automated COVID-19 diagnosis in an easily applicable and fast yet accurate way.