In this work, CT-xCOV, an explainable framework for COVID-19 diagnosis using Deep Learning (DL) on CT-scans is developed. CT-xCOV adopts an end-to-end approach from lung segmentation to COVID-19 detection and explanations of the detection model's prediction. For lung segmentation, we used the well-known U-Net model. For COVID-19 detection, we compared three different CNN architectures: a standard CNN, ResNet50, and DenseNet121. After the detection, visual and textual explanations are provided. For visual explanations, we applied three different XAI techniques, namely, Grad-Cam, Integrated Gradient (IG), and LIME. Textual explanations are added by computing the percentage of infection by lungs. To assess the performance of the used XAI techniques, we propose a ground-truth-based evaluation method, measuring the similarity between the visualization outputs and the ground-truth infections. The performed experiments show that the applied DL models achieved good results. The U-Net segmentation model achieved a high Dice coefficient (98%). The performance of our proposed classification model (standard CNN) was validated using 5-fold cross-validation (acc of 98.40% and f1-score 98.23%). Lastly, the results of the comparison of XAI techniques show that Grad-Cam gives the best explanations compared to LIME and IG, by achieving a Dice coefficient of 55%, on COVID-19 positive scans, compared to 29% and 24% obtained by IG and LIME respectively. The code and the dataset used in this paper are available in the GitHub repository [1].