The condensin protein complex plays a key role in the structural organization of genomes. How the ATPase activity of its SMC subunits drives large-scale changes in chromosome topology has remained unknown. Here we reconstruct, at near-atomic resolution, the sequence of events that take place during the condensin ATPase cycle. We show that ATP binding induces a conformational switch in the Smc4 head domain that releases its hitherto undescribed interaction with the Ycs4 HEAT-repeat subunit and promotes its engagement with the Smc2 head into an asymmetric heterodimer. SMC head dimerization subsequently enables nucleotide binding at the second active site and disengages the Brn1 kleisin subunit from the Smc2 coiled coil to open the condensin ring. These large-scale transitions in the condensin architecture lay out a mechanistic path for its ability to extrude DNA helices into large loop structures.