The formation of ordered one-dimensional graphene ripples of nanometer periodicity with exceptionally large buckling has recently been observed on Ir(001). In this phase, chemisorbed lines of graphene, only a few atoms wide, strongly bind to the substrate along Ir[010], while the whole graphene film markedly buckles between these periodic lines, forming regular ripples along Ir[100]. We have performed a dispersion-corrected density functional theory study to investigate the microscopic mechanisms responsible for the formation of this new phase. Based on the calculated trends of the chemisorption and rippling energies, the occurrence of a buckled chemisorbed phase with a specific nanoscale periodicity is explained. We have also examined how the increased curvature of graphene affects its electronic structure and chemisorption energy on Ir, finding a new feature in the conduction density-of-states spectrum close to the Fermi energy. The corresponding states are identified as the ones largely responsible for the strong local chemisorption of graphene.