Breast density is a significant risk factor for breast cancer and can impact the sensitivity of screening mammography. Area-based breast density measurements may not provide an accurate representation of the tissue distribution, therefore volumetric breast density (VBD) measurements are preferred. Dual-energy mammography enables volumetric measurements without additional assumptions about breast shape. In this work we evaluated the performance of a dual-energy decomposition technique for determining VBD by applying it to virtual anthropomorphic phantoms. The dual-energy decomposition formalism was used to quantify VBD on simulated dual-energy images of anthropomorphic virtual phantoms with known tissue distributions. We simulated 150 phantoms with volumes ranging from 50 to 709mL and VBD ranging from 15% to 60%. Using these results, we validated a correction for the presence of skin and assessed the method's intrinsic bias and variability. As a proof of concept, the method was applied to 14 sets of clinical dual-energy images, and the resulting breast densities were compared to magnetic resonance imaging (MRI) measurements. Virtual phantom VBD measurements exhibited a strong correlation (Pearson's ) with nominal values. The proposed skin correction eliminated the variability due to breast size and reduced the bias in VBD to a constant value of -2%. Disagreement between clinical VBD measurements using MRI and dual-energy mammography was under 10%, and the difference in the distributions was statistically non-significant. VBD measurements in both modalities had a moderate correlation (Spearman's =0.68). Our results in virtual phantoms indicate that the material decomposition method can produce accurate VBD measurements if the presence of a third material (skin) is considered. The results from our proof of concept showed agreement between MRI and dual-energy mammography VBD. Assessment of VBD using dual-energy images could provide complementary information in dual-energy mammography and tomosynthesis examinations.