Background: Recent studies have shown that epicardial adipose tissue (EAT) is an independent atrial fibrillation (AF) prognostic marker and has influence on the myocardial function. In computed tomography (CT), EAT volume (EATv) and density (EATd) are parameters that are often used to quantify EAT. While increased EATv has been found to correlate with the prevalence and the recurrence of AF after ablation therapy, higher EATd correlates with inflammation due to arrest of lipid maturation and with high risk of plaque presence and plaque progression. Automation of the quantification task diminishes the variability in readings introduced by different observers in manual quantification and results in high reproducibility of studies and less time-consuming analysis. Our objective is to develop a fully automated quantification of EATv and EATd using a deep learning (DL) framework. Methods: We proposed a framework that consists of image classification and segmentation DL models and performs the task of selecting images with EAT from all the CT images acquired for a patient, and the task of segmenting the EAT from the output images of the preceding task. EATv and EATd are estimated using the segmentation masks to define the region of interest. For our experiments, a 300-patient dataset was divided into two subsets, each consisting of 150 patients: Dataset 1 (41,979 CT slices) for training the DL models, and Dataset 2 (36,428 CT slices) for evaluating the quantification of EATv and EATd. Results: The classification model achieved accuracies of 98% for precision, recall and F{}_1 scores, and the segmentation model achieved accuracies in terms of mean (\pm std.) and median dice similarity coefficient scores of 0.844 (\pm 0.19) and 0.84, respectively. Using the evaluation set (Dataset 2), our approach resulted in a Pearson correlation coefficient of 0.971 (R{}^2 = 0.943) between the label and predicted EATv, and the correlation coefficient of 0.972 (R{}^2 = 0.945) between the label and predicted EATd. Conclusions: We proposed a framework that provides a fast and robust strategy for accurate EAT segmentation, and volume (EATv) and attenuation (EATd) quantification tasks. The framework will be useful to clinicians and other practitioners for carrying out reproducible EAT quantification at patient level or for large cohorts and high-throughput projects.