Defects in nuclear morphology often correlate with the onset of disease, including cancer, progeria, cardiomyopathy, and muscular dystrophy. However, the mechanism by which a cell controls its nuclear shape is unknown. Here, we use adhesive micropatterned surfaces to control the overall shape of fibroblasts and find that the shape of the nucleus is tightly regulated by the underlying cell adhesion geometry. We found that this regulation occurs through a dome-like actin cap that covers the top of the nucleus. This cap is composed of contractile actin filament bundles containing phosphorylated myosin, which form a highly organized, dynamic, and oriented structure in a wide variety of cells. The perinuclear actin cap is specifically disorganized or eliminated by inhibition of actomyosin contractility and rupture of the LINC complexes, which connect the nucleus to the actin cap. The organization of this actin cap and its nuclear shape-determining function are disrupted in cells from mouse models of accelerated aging (progeria) and muscular dystrophy with distorted nuclei caused by alterations of A-type lamins. These results highlight the interplay between cell shape, nuclear shape, and cell adhesion mediated by the perinuclear actin cap.