Rheumatoid arthritis and hand osteoarthritis are two different arthritis that causes pain, function limitation, and permanent joint damage in the hands. Plain hand radiographs are the most commonly used imaging methods for the diagnosis, differential diagnosis, and monitoring of rheumatoid arthritis and osteoarthritis. In this retrospective study, the You Only Look Once (YOLO) algorithm was used to obtain hand images from original radiographs without data loss, and classification was made by applying transfer learning with a pre-trained VGG-16 network. The data augmentation method was applied during training. The results of the study were evaluated with performance metrics such as accuracy, sensitivity, specificity, and precision calculated from the confusion matrix, and AUC (area under the ROC curve) calculated from ROC (receiver operating characteristic) curve. In the classification of rheumatoid arthritis and normal hand radiographs, 90.7%, 92.6%, 88.7%, 89.3%, and 0.97 accuracy, sensitivity, specificity, precision, and AUC results, respectively, and in the classification of osteoarthritis and normal hand radiographs, 90.8%, 91.4%, 90.2%, 91.4%, and 0.96 accuracy, sensitivity, specificity, precision, and AUC results were obtained, respectively. In the classification of rheumatoid arthritis, osteoarthritis, and normal hand radiographs, an 80.6% accuracy result was obtained. In this study, to develop an end-to-end computerized method, the YOLOv4 algorithm was used for object detection, and a pre-trained VGG-16 network was used for the classification of hand radiographs. This computer-aided diagnosis method can assist clinicians in interpreting hand radiographs, especially in rheumatoid arthritis and osteoarthritis.