Mammalian genomes are organized into megabase-scale topologically associated domains (TADs). We demonstrate that disruption of TADs can rewire long-range regulatory architecture and result in pathogenic phenotypes. We show that distinct human limb malformations are caused by deletions, inversions, or duplications altering the structure of the TAD-spanning WNT6/IHH/EPHA4/PAX3 locus. Using CRISPR/Cas genome editing, we generated mice with corresponding rearrangements. Both in mouse limb tissue and patient-derived fibroblasts, disease-relevant structural changes cause ectopic interactions between promoters and non-coding DNA, and a cluster of limb enhancers normally associated with Epha4 is misplaced relative to TAD boundaries and drives ectopic limb expression of another gene in the locus. This rewiring occurred only if the variant disrupted a CTCF-associated boundary domain. Our results demonstrate the functional importance of TADs for orchestrating gene expression via genome architecture and indicate criteria for predicting the pathogenicity of human structural variants, particularly in non-coding regions of the human genome.