The Transforming Growth Factor-β (TGFβ) signaling pathway controls transcription by regulating enhancer activity. How TGFβ-regulated enhancers are selected and what chromatin changes are associated with TGFβ-dependent enhancers regulation are still unclear. Here we report that TGFβ treatment triggers fast and widespread increase in chromatin accessibility in about 80\% of the enhancers of normal mouse mammary epithelial-gland cells, irrespective of whether they are activated, repressed or not regulated by TGFβ. This enhancer opening depends on both the canonical and non-canonical TGFβ pathways. Most TGFβ-regulated genes are located around enhancers regulated in the same way, often creating domains of several co-regulated genes that we term TGFβ regulatory domains (TRD). CRISPR-mediated inactivation of enhancers within TRDs impairs TGFβ-dependent regulation of all co-regulated genes, demonstrating that enhancer targeting is more promiscuous than previously anticipated. The area of TRD influence is restricted by topologically associating domains (TADs) borders, causing a bias towards co-regulation within TADs.