We report the reprogramming of nonheme iron enzymes to catalyze an abiological C(sp3)‒H azidation reaction through iron-catalyzed radical relay. This biocatalytic transformation uses amidyl radicals as hydrogen atom abstractors and Fe(III)‒N3 intermediates as radical trapping agents. We established a high-throughput screening platform based on click chemistry for rapid evolution of the catalytic performance of identified enzymes. The final optimized variants deliver a range of azidation products with up to 10,600 total turnovers and 93% enantiomeric excess. Given the prevalence of radical relay reactions in organic synthesis and the diversity of nonheme iron enzymes, we envision that this discovery will stimulate future development of metalloenzyme catalysts for synthetically useful transformations unexplored by natural evolution.