Patients with obstructive sleep apnea (OSA) show neuropsychological impairments ranging from vigilance decrements, attentional lapses and memory gaps to decreased motor coordination, but their cognitive profile, and the origin of the impairments, remain unclear. We sought to establish the neuropsychological profile of 16 newly diagnosed apneics and to highlight both their morphological and functional brain abnormalities. We used an extensive neuropsychological test battery to investigate attention and vigilance, executive functions, episodic memory and motor domains. For brain imaging, we used the optimized voxel-based morphometry procedure for the MRI data, resting-state 18F-fluoro-2-deoxy-D-Glucose positron emission tomography (18FDG-PET) with correction for partial volume effects (PVEs) and voxel-based analyses. In terms of neurobehavioral performance, our patients displayed objective daytime somnolence but little impairment in memory and motor domains. Cerebral data revealed gray matter loss in the frontal and temporo–parieto–occipital cortices, the thalamus, hippocampal region, some basal ganglia and cerebellar regions, mainly in the right hemisphere. The decrease in brain metabolism was also right-lateralized, but more restricted than the gray matter density changes, and involved the precuneus, the middle and posterior cingulate gyrus, and the parieto–occipital cortex, as well as the prefrontal cortex. To conclude, despite the presence of only minor memory and motor impairments, our patients displayed significant cerebral changes in terms of both gray matter density and metabolic levels, and may have benefited from cognitive reserve and compensatory mechanisms. Thus, cerebral changes in OSA patients may precede the onset of notable neuropsychological consequences.