Spatiotemporal allostery is the source of complex but ordered biological phenomena. To identify the structural basis for allostery that drives the cyanobacterial circadian clock, we crystallized the clock protein KaiC in four distinct states, which cover a whole cycle of phosphor-transfer events at Ser431 and Thr432. The minimal set of allosteric events required for oscillatory nature is a bidirectional coupling between the coil-to-helix transition of the Ser431-dependent phospho-switch in the C-terminal domain of KaiC and adenosine 5'-diphosphate release from its N-terminal domain during adenosine triphosphatase cycle. An engineered KaiC protein oscillator consisting of a minimal set of the identified master allosteric events exhibited a monophosphorylation cycle of Ser431 with a temperature-compensated circadian period, providing design principles for simple posttranslational biochemical circadian oscillators.