Complexes containing a pair of structural maintenance of chromosomes (SMC) family proteins are fundamental for the three-dimensional (3D) organization of genomes in all domains of life. The eukaryotic SMC complexes cohesin and condensin are thought to fold interphase and mitotic chromosomes, respectively, into large loop domains, although the underlying molecular mechanisms have remained unknown. We used cryo-EM to investigate the nucleotide-driven reaction cycle of condensin from the budding yeast Saccharomyces cerevisiae. Our structures of the five-subunit condensin holo complex at different functional stages suggest that ATP binding induces the transition of the SMC coiled coils from a folded-rod conformation into a more open architecture. ATP binding simultaneously triggers the exchange of the two HEAT-repeat subunits bound to the SMC ATPase head domains. We propose that these steps result in the interconversion of DNA-binding sites in the catalytic core of condensin, forming the basis of the DNA translocation and loop-extrusion activities.