Enhancers and promoters interact in three-dimensional (3D) chromatin structures to regulate gene expression. Here we characterize the mechanisms that drive the formation and function of these structures in a lymphoid-to-myeloid transdifferentiation 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. Multi-way interaction analyses and computational modeling show that tissue-specific gene loci are organized into chromatin hubs, characterized by cooperative interactions between multiple enhancers, promoters and CTCF-binding sites. While depletion of CTCF strongly impairs the formation of these chromatin hubs, the effects of CTCF depletion on gene expression are modest and can be explained by rewired enhancer-promoter interactions. These findings demonstrate a role for enhancer-promoter interactions in gene regulation that is independent of cooperative interactions in chromatin hubs. Together, these results contribute to our understanding of the structure-function relationship of the genome during cellular differentiation.