Enhancers and promoters interact in 3D chromatin structures to regulate gene expression. Here, we characterize the mechanisms that drive the formation of these structures and their function in gene regulation in a lymphoid-to-myeloid differentiation system. Based on analyses at base-pair resolution, we demonstrate a close correlation between binding of regulatory proteins, formation of chromatin interactions, and gene expression. Integration of single-allele topologies and computational modeling shows that tissue-specific gene loci are organized into chromatin hubs, characterized by cooperative interactions between multiple enhancers, promoters, and CTCF-binding sites. Depletion of CTCF leads to a near-complete loss of these structures, which indicates that CTCF-mediated interactions provide a scaffold for chromatin hub formation. In contrast, the effects of CTCF depletion on gene expression are mild and can be explained by rewired enhancer-promoter interactions. This demonstrates an instructive role for enhancer-promoter interactions in gene regulation, which does not depend on cooperative interactions in chromatin hubs. Together, these results contribute to a mechanistic understanding of the structure-function relationship of the genome during cellular differentiation.