Theoretical studies have demonstrated that selection will favor increased migration when fitnesses vary both temporally and spatially, but it is far from clear how pervasive those theoretical conditions are in nature. While consumer-resource interactions are omnipresent in nature and can generate spatial and temporal variation, it is unknown even in theory whether these dynamics favor the evolution of migration. We develop a mathematical model to address whether and how migration evolves when variability in fitness is determined at least in part by consumer-resource coevolutionary interactions. Our analyses show that such interactions can drive the evolution of migration in the resource, consumer, or both species and thus supplies a general explanation for the pervasiveness of migration. Over short time scales, we show the direction of change in migration rate is determined primarily by the state of local adaptation of the species involved: rates increase when a species is locally maladapted and decrease when locally adapted. Our results reveal that long-term evolutionary trends in migration rates can differ dramatically depending on the strength or weakness of interspecific interactions and suggest an explanation for the evolutionary divergence of migration rates among interacting species.