Balanced chromosomal rearrangements (BCRs), including inversions, translocations, and insertions, reorganize large sections of the genome and contribute substantial risk for developmental disorders (DDs). However, the rarity and lack of systematic screening for BCRs in the population has precluded unbiased analyses of the genomic features and mechanisms associated with risk for DDs versus normal developmental outcomes. Here, we sequenced and analyzed 1,420 BCR breakpoints across 710 individuals, including 406 DD cases and the first large-scale collection of 304 control BCR carriers. We found that BCRs were not more likely to disrupt genes in DD cases than controls, but were seven-fold more likely to disrupt genes associated with dominant DDs (21.3% of cases vs. 3.4% of controls; P = 1.60×10−12). Moreover, BCRs that did not disrupt a known DD gene were significantly enriched for breakpoints that altered topologically associated domains (TADs) containing dominant DD genes in cases compared to controls (odds ratio [OR] = 1.43, P = 0.036). We discovered six TADs enriched for noncoding BCRs (false discovery rate < 0.1) that contained known DD genes (MEF2C, FOXG1, SOX9, BCL11A, BCL11B, and SATB2) and represent candidate pathogenic long-range positional effect (LRPE) loci. These six TADs were collectively disrupted in 7.4% of the DD cohort. Phased Hi-C analyses of five cases with noncoding BCR breakpoints localized to one of these putative LRPEs, the 5q14.3 TAD encompassing MEF2C, confirmed extensive disruption to local 3D chromatin structures and reduced frequency of contact between the MEF2C promoter and annotated enhancers. We further identified six genomic features enriched in TADs preferentially disrupted by noncoding BCRs in DD cases versus controls and used these features to build a model to predict TADs at risk for LRPEs across the genome. These results emphasize the potential impact of noncoding structural variants to cause LRPEs in unsolved DD cases, as well as the complex interaction of features associated with predicting three-dimensional chromatin structures intolerant to disruption.