Annotation of cis-regulatory elements that drive transcriptional dysregulation in cancer cells is critical to understanding tumor biology. Herein, we present matched chromatin accessibility (single-cell assay for transposase-accessible chromatin by sequencing [scATAC-seq]) and transcriptome (single-cell RNA sequencing [scRNA-seq]) profiles at single-cell resolution from human breast tumors and healthy mammary tissues processed immediately following surgical resection. We identify the most likely cell of origin for subtype-specific breast tumors and implement linear mixed-effects modeling to quantify associations between regulatory elements and gene expression in malignant versus normal cells. These data unveil cancer-specific regulatory elements and putative silencer-to-enhancer switching events in cells that lead to the upregulation of clinically relevant oncogenes. In addition, we generate matched scATAC-seq and scRNA-seq profiles for breast cancer cell lines, revealing a conserved oncogenic gene expression program between in vitro and in vivo cells. This work highlights the importance of non-coding regulatory mechanisms that underlie oncogenic processes and the ability of single-cell multi-omics to define the regulatory logic of cancer cells.