Background parenchymal enhancement (BPE) observed in breast dynamic contrast enhanced magnetic resonance imaging (DCE-MRI) has been identified as an important biomarker associated with risk for developing breast cancer. In this study, we present a fully automated framework for quantification of BPE. We initially segmented fibroglandular tissue (FGT) of the breasts using an improved version of an existing method. Subsequently, we computed BPEabs (volume of the enhancing tissue), BPErf (BPEabs divided by FGT volume) and BPErb (BPEabs divided by breast volume), using different relative enhancement threshold values between 1% and 100%. To evaluate and compare the previous and improved FGT segmentation methods, we used 20 breast DCE-MRI scans and we computed Dice similarity coefficient (DSC) values with respect to manual segmentations. For evaluation of the BPE quantification, we used a dataset of 95 breast DCE-MRI scans. Two radiologists, in individual reading sessions, visually analyzed the dataset and categorized each breast into minimal, mild, moderate and marked BPE. To measure the correlation between automated BPE values to the radiologists' assessments, we converted these values into ordinal categories and we used Spearman's rho as a measure of correlation. According to our results, the new segmentation method obtained an average DSC of 0.81 0.09, which was significantly higher (p<0.001) compared to the previous method (0.76 0.10). The highest correlation values between automated BPE categories and radiologists' assessments were obtained with the BPErf measurement (r=0.55, r=0.49, p<0.001 for both), while the correlation between the scores given by the two radiologists was 0.82 (p<0.001). The presented framework can be used to systematically investigate the correlation between BPE and risk in large screening cohorts.