Flavoprotein monooxygenases are a versatile group of enzymes for biocatalytic transformations. Among these, group E monooxygenases (GEMs) catalyze enantioselective epoxidation and sulfoxidation reactions. Here, we describe the crystal structure of an indole monooxygenase from the bacterium Variovorax paradoxus EPS, a GEM designated as VpIndA1. Complex structures with substrates reveal productive binding modes that, in conjunction with force-field calculations and rapid mixing kinetics, reveal the structural basis of substrate and stereoselectivity. Structure-based redesign of the substrate cavity yielded variants with new substrate selectivity (for sulfoxidation of benzyl phenyl sulfide) or with greatly enhanced stereoselectivity (from 35.1 % to 99.8 % ee for production of (1S,2R)-indene oxide). This first determination of the substrate binding mode of GEMs combined with structure-function relationships opens the door for structure-based design of these powerful biocatalysts.