Humans need about seven to nine hours of sleep per night. Sleep habits are heritable, associated with brain function and structure, and intrinsically related to well-being, mental, and physical health. However, the biological basis of the interplay of sleep and health is incompletely understood. Here we show, by combining neuroimaging and behavioral genetic approaches in two independent large-scale datasets (HCP (n = 1106), age range: 22-37, eNKI (n = 783), age range: 12-85), that sleep, mental, and physical health have a shared neurobiological basis in grey matter anatomy; and that these relationships are driven by shared genetic factors. Though local associations between sleep and cortical thickness were inconsistent across samples, we identified two robust latent components, highlighting the multivariate interdigitation of sleep, intelligence, BMI, depression, and macroscale cortical structure. Our observations provide a system-level perspective on the interrelation of sleep, mental, and physical conditions, anchored in grey-matter neuroanatomy.