Some individuals are better at learning about rewarding situations, whereas others are inclined to avoid punishments (i.e., enhanced approach or avoidance learning, respectively). In reinforcement learning, action values are increased when outcomes are better than predicted (positive prediction errors [PEs]) and decreased for worse than predicted outcomes (negative PEs). Because actions with high and low values are approached and avoided, respectively, individual differences in the neural encoding of PEs may influence the balance between approach-avoidance learning. Recent correlational approaches also indicate that biases in approach-avoidance learning involve hemispheric asymmetries in dopamine function. However, the computational and neural mechanisms underpinning such learning biases remain unknown. Here we assessed hemispheric reward asymmetry in striatal activity in 34 human participants who performed a task involving rewards and punishments. We show that the relative difference in reward response between hemispheres relates to individual biases in approach-avoidance learning. Moreover, using a computational modeling approach, we demonstrate that better encoding of positive (vs negative) PEs in dopaminergic midbrain regions is associated with better approach (vs avoidance) learning, specifically in participants with larger reward responses in the left (vs right) ventral striatum. Thus, individual dispositions or traits may be determined by neural processes acting to constrain learning about specific aspects of the world.