We report a strategy for effecting catalytic, enantioselective carbocationic rearrangements through the intermediacy of alkyl iodanes as stereodefined carbocation equivalents. Asymmetric Wagner-Meerwein rearrangements of β-substituted styrenes are catalyzed by the C2-symmetric aryl iodide 1 to provide access to enantioenriched 1,3-difluorinated molecules possessing interesting and well-defined conformational properties. Hammett and kinetic isotope effect studies, in combination with computational investigations, reveal that two different mechanisms are operative in these rearrangement reactions, with the pathway depending on the identity of the migrating group. In reactions involving alkyl-group migration, intermolecular fluoride attack is product- and enantio-determining. In contrast, reactions in which aryl rearrangement occurs proceed through an enantiodetermining intramolecular 1,2-migration prior to fluorination. The fact that both pathways are promoted by the same chiral aryl iodide catalyst with high enantioselectivity provides a compelling illustration of generality across reaction mechanisms in asymmetric catalysis.