Background: We sought to gain new insight into triple-negative breast cancer (TNBC), an aggressive, clinically distinct subgroup of breast cancers, by applying a sequence of computational approaches to tumor segmentation, three-dimensional anatomic characterization, and tumor subtyping. We extracted algorithmically-derived quantitative imaging (radiomics) features from each TNBC lesion in breast magnetic resonance imaging (MRI) to identify underlying subtypes. Methods: We evaluated tumors on pre-treatment, post-contrast MRI from 90 patients with non-metastatic TNBC. We employed active contour segmentation and semi-automated identification of tumor regions-of-interest. We extracted 900 radiomics features from each segmented tumor using an algorithm that characterizes the size, shape, texture, and edge sharpness of tumors at the voxel level. We applied k-means consensus clustering, a statistical tool for unsupervised discovery, and performed 1000 bootstraps with resampling on the feature vectors to examine all resulting clusters from k=2 to 10. Based on two diagnostic metrics of consensus stability, we selected the optimum cluster number. We performed Significance Analysis of Microarrays to identify statistically significant radiomics features for each cluster. Results: We identified three distinct image-based clusters in 117 tumors from 90 TNBC patients (multifocal lesions in n=13). Cluster 1 (n=97) was distinguished by 330 radiomics features (False Discovery Rate [FDR] <5%) and Cluster 2 (n=13) by 85 features (FDR<5%), whereas Cluster 3 (n=7) was not significantly associated with features. Clinical characteristics did not differ across the three clusters, with mean age (49.1±11.7) and clinical stage distributions (stage I: 20.7%, II: 55.4%, III: 23.9%) for the cohort mirroring those of individual clusters. Among those who received neoadjuvant therapy, we observed pathologic complete response in 50% (23 of 46, 95% CI, 0.36-0.64) of patients in Cluster 1, 83% (5 of 6, 95% CI, 0.54-1.0) in Cluster 2, and 0% (0 of 3) in Cluster 3. Conclusions: Radiomics features providing voxel-level characteristics of tumor morphology differentiated TNBC into three distinct subtypes. These subtypes, defined by radiomics biomarkers, may be associated with clinical response to neoadjuvant therapy.