Because eye movements are a fundamental tool for spatial exploration, we hypothesized that the neural bases of these movements in humans should be under right cerebral dominance, as already described for spatial attention. We used functional magnetic resonance imaging in 27 right-handed participants who alternated central fixation with either large or small visually guided saccades (VGS), equally performed in both directions. Hemispheric functional asymmetry was analyzed to identify whether brain regions showing VGS activation elicited hemispheric asymmetries. Hemispheric anatomical asymmetry was also estimated to assess its influence on the VGS functional lateralization. Right asymmetrical activations of a saccadic/attentional system were observed in the lateral frontal eye fields (FEF), the anterior part of the intraparietal sulcus (aIPS), the posterior third of the superior temporal sulcus (STS), the occipitotemporal junction (MT/V5 area), the middle occipital gyrus, and medially along the calcarine fissure (V1). The present rightward functional asymmetries were not related to differences in gray matter (GM) density/sulci positions between right and left hemispheres in the precentral, intraparietal, superior temporal, and extrastriate regions. Only V1 asymmetries were explained for almost 20% of the variance by a difference in the position of the right and left calcarine fissures. Left asymmetrical activations of a saccadic motor system were observed in the medial FEF and in the motor strip eye field along the Rolando sulcus. They were not explained by GM asymmetries. We suggest that the leftward saccadic motor asymmetry is part of a general dominance of the left motor cortex in right-handers, which must include an effect of sighting dominance. Our results demonstrate that, although bilateral by nature, the brain network involved in the execution of VGSs, irrespective of their direction, presented specific right and left asymmetries that were not related to anatomical differences in sulci positions.