Extensive prior research focused on somatic copy-number alterations (SCNAs) affecting cancer genes, yet the extent to which recurrent SCNAs exert their influence through rearrangement of cis-regulatory elements (CREs) remains unclear. Here we present a framework for inferring cancer-related gene overexpression resulting from CRE reorganization (e.g., enhancer hijacking) by integrating SCNAs, gene expression data and information on topologically associating domains (TADs). Analysis of 7,416 cancer genomes uncovered several pan-cancer candidate genes, including IRS4, SMARCA1 and TERT. We demonstrate that IRS4 overexpression in lung cancer is associated with recurrent deletions in cis, and we present evidence supporting a tumor-promoting role. We additionally pursued cancer-type-specific analyses and uncovered IGF2 as a target for enhancer hijacking in colorectal cancer. Recurrent tandem duplications intersecting with a TAD boundary mediate de novo formation of a 3D contact domain comprising IGF2 and a lineage-specific super-enhancer, resulting in high-level gene activation. Our framework enables systematic inference of CRE rearrangements mediating dysregulation in cancer.