Nanoscale structures were produced on silicon surfaces by low-energy oxygen ion irradiation: periodic rippled or terraced patterns formed spontaneously, depending on the chosen combination of beam incidence angle and ion fluence. Atomic force microscopy image processing and analysis accurately described the obtained nanotopographies. Graphene monolayers grown by chemical vapour deposition were transferred onto the nanostructured silicon surfaces. The interfacial interaction between the textured surface and the deposited graphene governs the conformation of the thin carbon layer; the resulting different degree of regularity and conformality of the substrate-induced graphene corrugations was studied and it was related to the distinctive topographical features of the silicon nanostructures. Raman spectroscopy revealed specific features of the strain caused by the alternating suspension and contact with the underlying nanostructures and the consequent modulation of the silicon-graphene interaction. Lay Description In the field of nanosciences, nanotechnologies and advanced materials, it is pivotal to produce and integrate nanostructures in a controlled, cost-effective and possibly high-throughput manner. Currently, the surface nanopatterning by ion beam irradiation (IBI) is showing its potential in overcoming some of the limits that characterize the conventional lithographic techniques. IBI can produce self-organized and regular patterns of nanostructures, such as ripples, dots, and holes, having heights and lateral periodicities in a pre-defined range. The nanopatterns can develop over large surface areas of a broad class of materials and have been tested for different applications, e.g. microelectronic device fabrication, catalysis, nanoscale magnetism, surface-enhanced Raman scattering. Also, the ion-induced patterns allowed the control of physical properties such as wettability, reflectance, and photoluminescence. As a whole, this is a highly dynamic and continuously evolving field. Graphene was first obtained from bulk graphite by mechanical exfoliation; remarkable mechanical, thermal and optical properties came to light; they make graphene an ideal material for sensing. Also, the research on graphene paves the way for basic and applied studies on other ultrathin thickness materials, such as monolayer transition metal dichalcogenide or monolayer metal oxide, which also show peculiar properties as compared to their bulk version. Since graphene is a zero-gap semi-metal, a finite energy gap must be open to engineer graphene-based electronic devices. At this aim, researchers can take advantage of the mechanical properties of graphene, since its out-of-plane deformation can favourably modify its electronic structure. While the spontaneous, random self-folding of graphene to form wrinkles has thermodynamics reasons and is unavoidable above a certain material length, the interactions between graphene and substrates can generate, in principle, designed wrinkled structures. Therefore, a field of study has emerged, focused on the control and tuning of the geometry of graphene corrugations and their influence on specific physical and chemical properties. To the best of our knowledge, this work studies for the first time the geometry and strain in graphene wrinkles induced by silicon substrates that were suitably nanopatterned by ion beam irradiation.