Structural variants (SVs) involving enhancer hijacking can rewire chromatin topologies to cause oncogene activation in human cancers including hematologic malignancies; however, due to the lack of tools to assess their effects on gene regulation and chromatin organization, the molecular determinants for the functional output of enhancer hijacking remain poorly understood. Here, we developed a multimodal approach to integrate genome sequencing, chromosome conformation, chromatin state, and transcriptomic alteration for quantitative analysis of transcriptional effects and structural reorganization imposed by SVs in leukemic genomes. We identified known and new pathogenic SVs including recurrent t(5;14) translocations that cause the hijacking of BCL11B enhancers for the allele-specific activation of TLX3 in a subtype of pediatric leukemia. Epigenetic perturbation of SV-hijacked BCL11B enhancers impairs TLX3 transcription required for the growth of t(5;14) leukemia cells. By CRISPR engineering of patient-derived t(5;14) in isogenic leukemia cells, we uncovered a new mechanism whereby the transcriptional output of SV-induced BCL11B enhancer hijacking is dependent on the loss of DNA hypermethylation at the TLX3 promoter. Our results highlight the importance of the cooperation between genetic alteration and permissive chromatin as a critical determinant of SV-mediated oncogene activation, with implications for understanding aberrant gene transcription following epigenetic therapies in leukemia patients. Hence, leveraging the interdependency of genetic alteration on chromatin variation may provide new opportunities to reprogram gene regulation as targeted interventions in human disease.