What is the relationship between action and emotion? People tend to perform approach actions with their dominant hand and avoidance actions with their nondominant hand. In right-handers, the left frontal lobe is specialized for approach-motivational states, and the right frontal lobe for avoidance-motivational states. Are brain areas that support affective motivation functionally related to areas that support approach- and avoidance-related motor actions? If so, hemispheric specialization for motivation should covary with hemispheric specialization for motor control. Here we tested this prediction, using electroencephalography (EEG) to compare resting alpha-band power in right- and left-handers. Hemispheric asymmetries in alpha-power were related to Behavioral Activation System (BAS) scores, which index approach-motivational tendencies. Results show that the pattern observed in right-handers reverses in left-handers, whose right hemisphere is specialized for both approach motivation and for control of dominant-hand actions. This anatomical covariation suggests a functional link between affective motivation and motor control.