Enhancer hijacking, caused by structural alterations on chromosomes as well as extrachromosomal DNA (ecDNA), is a common cancer driver event. The complexity and ubiquity of structural alterations in cancer genomes make it difficult to identify enhancer hijacking using genome sequencing alone. Here we describe a 3D genomics-based analysis called HAPI (Highly Active Promoter Interactions) to characterize enhancer hijacking caused by structural alterations. HAPI analysis of HiChIP data from 34 cancer cell lines identified novel enhancer hijacking events that involve chromosomal rearrangements and activate both known and potentially novel oncogenes such as MYC, CCND1, ETV1, CRKL, and ID4, which we validated using CRISPRi assays and RNA-seq analysis. Furthermore, we found that ecDNAs often contain multiple oncogenes from different chromosomes, which causes nested enhancer hijacking among them. We found that ecDNAs containing MYC often harbor additional oncogenes from other chromosomes such as CDX2, ERBB2, or CD44 that co-opt MYC's enhancers for their overexpression, which we validated using dual-color DNA FISH and CRISPRi assays. These enhancer hijacking events involving multiple oncogenes on ecDNAs have important implications for therapeutic strategies that either target the co-opting oncogenes or the hijacked enhancers. Our publicly available HAPI analysis tool provides a robust strategy to detect enhancer hijacking and reveals novel insights into oncogene activation caused by chromosomal and extrachromosomal structural alterations.