Associative theory postulates that learning the consequences of our actions in a given context is represented in the brain as stimulus-response-outcome associations that evolve according to prediction-error signals (the discrepancy between the observed and predicted outcome). We tested the theory on brain functional magnetic resonance imaging data acquired from human participants learning arbitrary visuomotor associations. We developed a novel task that systematically manipulated learning and induced highly reproducible performances. This granted the validation of the model-based results and an in-depth analysis of the brain signals in representative single trials. Consistent with the Rescorla-Wagner model, prediction-error signals are computed in the human brain and selectively engage the ventral striatum. In addition, we found evidence of computations not formally predicted by the Rescorla-Wagner model. The dorsal fronto-parietal network, the dorsal striatum, and the ventrolateral prefrontal cortex are activated both on the incorrect and first correct trials and may reflect the processing of relevant visuomotor mappings during the early phases of learning. The left dorsolateral prefrontal cortex is selectively activated on the first correct outcome. The results provide quantitative evidence of the neural computations mediating arbitrary visuomotor learning and suggest new directions for future computational models.