The ability to reason and problem-solve in novel situations, as measured by the Raven's Advanced Progressive Matrices (RAPM), is highly predictive of both cognitive task performance and real-world outcomes. Here we provide evidence that RAPM performance depends on the ability to reallocate attention in response to self-generated feedback about progress. We propose that such an ability is underpinned by the basal ganglia nuclei, which are critically tied to both reward processing and cognitive control. This hypothesis was implemented in a neurocomputational model of the RAPM task, which was used to derive novel predictions at the behavioral and neural levels. These predictions were then verified in one neuroimaging and two behavioral experiments. Furthermore, an effective connectivity analysis of the neuroimaging data confirmed a role for the basal ganglia in modulating attention. Taken together, these results suggest that individual differences in a neural circuit related to reward processing underpin human fluid reasoning abilities.