Sensorimotor cortex mediates the formation of adaptation memory. Individuals differ in the rate at which they acquire, retain, and generalize adaptation. We present a mechanistic explanation of the neurochemical and computational causes of this variation in humans. Neuroimaging identified structural, functional and neurochemical covariates of a computational parameter that determines memory persistence. To establish causality, we increased sensorimotor cortex excitability during adaptation, using transcranial direct current stimulation. As predicted, this increased retention. Inter-individual variance in the stimulation-induced E:I increase predicted the computational change, which predicted the memory gain. These relations did not hold, and memory was unchanged, with stimulation applied before adaptation. This cognitive state dependent effect was modulated by the BDNF val66met genetic polymorphism. Memory was enhanced by stimulation in Val/Val carriers only, implicating a mechanistic role for activity-dependent BDNF secretion. Sensorimotor cortex E:I causally determines the time constant of memory persistence, explaining phenotypic variation in adaptation decay.