Two variant cohesin complexes containing SMC1, SMC3, RAD21 and either SA1 (also known as STAG1) or SA2 (also known as STAG2) are present in all cell types. We report here their genomic distribution and specific contributions to genome organization in human cells. Although both variants are found at CCCTC-binding factor (CTCF) sites, a distinct population of the SA2-containing cohesin complexes (hereafter referred to as cohesin-SA2) localize to enhancers lacking CTCF, are linked to tissue-specific transcription and cannot be replaced by the SA1-containing cohesin complex (cohesin-SA1) when SA2 is absent, a condition that has been observed in several tumors. Downregulation of each of these variants has different consequences for gene expression and genome architecture. Our results suggest that cohesin-SA1 preferentially contributes to the stabilization of topologically associating domain boundaries together with CTCF, whereas cohesin-SA2 promotes cell-type-specific contacts between enhancers and promoters independently of CTCF. Loss of cohesin-SA2 rewires local chromatin contacts and alters gene expression. These findings provide insights into how cohesin mediates chromosome folding and establish a novel framework to address the consequences of mutations in cohesin genes in cancer.