Coronavirus disease 2019 (COVID-2019), which emerged in Wuhan, China in 2019 and has spread rapidly all over the world since the beginning of 2020, has infected millions of people and caused many deaths. For this pandemic, which is still in effect, mobilization has started all over the world, and various restrictions and precautions have been taken to prevent the spread of this disease. In addition, infected people must be identified in order to control the infection. However, due to the inadequate number of Reverse Transcription Polymerase Chain Reaction (RT-PCR) tests, Chest computed tomography (CT) becomes a popular tool to assist the diagnosis of COVID-19. In this study, two deep learning architectures have been proposed that automatically detect positive COVID-19 cases using Chest CT X-ray images. Lung segmentation (preprocessing) in CT images, which are given as input to these proposed architectures, is performed automatically with Artificial Neural Networks (ANN). Since both architectures contain AlexNet architecture, the recommended method is a transfer learning application. However, the second proposed architecture is a hybrid structure as it contains a Bidirectional Long Short-Term Memories (BiLSTM) layer, which also takes into account the temporal properties. While the COVID-19 classification accuracy of the first architecture is 98.14%, this value is 98.70% in the second hybrid architecture. The results prove that the proposed architecture shows outstanding success in infection detection and, therefore this study contributes to previous studies in terms of both deep architectural design and high classification success.