One of the most difficult category learning problems for humans is learning nonnative speech categories. While feedback-based category training can enhance speech learning, the mechanisms underlying these benefits are unclear. In this functional magnetic resonance imaging study, we investigated neural and computational mechanisms underlying feedback-dependent speech category learning in adults. Positive feedback activated a large corticostriatal network including the dorsolateral prefrontal cortex, inferior parietal lobule, middle temporal gyrus, caudate, putamen, and the ventral striatum. Successful learning was contingent upon the activity of domain-general category learning systems: the fast-learning reflective system, involving the dorsolateral prefrontal cortex that develops and tests explicit rules based on the feedback content, and the slow-learning reflexive system, involving the putamen in which the stimuli are implicitly associated with category responses based on the reward value in feedback. Computational modeling of response strategies revealed significant use of reflective strategies early in training and greater use of reflexive strategies later in training. Reflexive strategy use was associated with increased activation in the putamen. Our results demonstrate a critical role for the reflexive corticostriatal learning system as a function of response strategy and proficiency during speech category learning.