Novel Coronavirus disease (COVID-19) is a highly contagious respiratory infection that has had devastating effects on the world. Recently, new COVID-19 variants are emerging making the situation more challenging and threatening. Evaluation and quantification of COVID-19 lung abnormalities based on chest Computed Tomography (CT) scans can help determining the disease stage, efficiently allocating limited healthcare resources, and making informed treatment decisions. During pandemic era, however, visual assessment and quantification of COVID-19 lung lesions by expert radiologists become expensive and prone to error, which raises an urgent quest to develop practical autonomous solutions. In this context, first, the paper introduces an open access COVID-19 CT segmentation dataset containing 433 CT images from 82 patients that have been annotated by an expert radiologist. Second, a Deep Neural Network (DNN)-based framework is proposed, referred to as the COVID-Rate, that autonomously segments lung abnormalities associated with COVID-19 from chest CT scans. Performance of the proposed COVID-Rate framework is evaluated through several experiments based on the introduced and external datasets. The results show a dice score of 0:802 and specificity and sensitivity of 0:997 and 0:832, respectively. Furthermore, the results indicate that the COVID-Rate model can efficiently segment COVID-19 lesions in both 2D CT images and whole lung volumes. Results on the external dataset illustrate generalization capabilities of the COVID-Rate model to CT images obtained from a different scanner.