The recent novel coronavirus (also known as COVID-19) has rapidly spread worldwide, causing an infectious respiratory disease that has killed hundreds of thousands and infected millions. While test kits are used for diagnosis of the disease, the process takes time and the test kits are limited in their availability. However, the COVID-19 disease is also diagnosable using radiological images taken through lung X-rays. This process is known to be both faster and more reliable as a form of identification and diagnosis. In this regard, the current study proposes an expert-designed system called COVIDetectioNet model, which utilizes features selected from combination of deep features for diagnosis of COVID-19. For this purpose, a pretrained Convolutional Neural Network (CNN)-based AlexNet architecture that employed the transfer learning approach, was used. The effective features that were selected using the Relief feature selection algorithm from all layers of the architecture were then classified using the Support Vector Machine (SVM) method. To verify the validity of the model proposed, a total of 6092 X-ray images, classified as Normal (healthy), COVID-19, and Pneumonia, were obtained from a combination of public datasets. In the experimental results, an accuracy of 99.18% was achieved using the model proposed. The results demonstrate that the proposed COVIDetectioNet model achieved a superior level of success when compared to previous studies.