Genome regulation requires control of chromosomal organization by SMC–kleisin complexes. The cohesin complex contains the Smc1 and Smc3 subunits which associate with the kleisin Scc1 to form a ring-shaped complex that can topologically engage chromatin to regulate chromatin structure. Release from chromatin involves opening of the ring at the Smc3–Scc1 interface in a reaction that is controlled by acetylation and engagement of the Smc ATPase head domains. To understand the underlying molecular mechanisms, we have determined the 3.2 Å cryo-EM structure of the ATPγS-bound, hetero-trimeric cohesin ATPase head module, and the 2.1 Å crystal structure of a nucleotide-free Smc1–Scc1 subcomplex from Saccharomyces cerevisiae and Chaetomium thermophilium. We found that ATP-binding and Smc1–Smc3 heterodimerization promote conformational changes within the ATPase which are transmitted to the Smc coiled-coil domains. Remodeling of the coiled-coil domain of Smc3 abrogates the binding surface for Scc1 thus leading to ring opening at the Smc3–Scc1 interface.