The DFT/vdW-WF2s1 method, recently developed to include the van der Waals interactions in the density functional theory and describe adsorption processes on metal surfaces by taking metal-screening effects into account, is applied to the case of the interaction of Xe and graphene with a transition-metal surface, namely, Ni(111). In general, the adsorption of rare-gas atoms on metal surfaces is important because it is prototypical for physisorption processes. Moreover, the interaction of graphene with Ni(111) is of great interest for practical applications, for instance concerning the efficient and large-scale production of high-quality graphene; from a theoretical point of view, it is particularly challenging, since it can be described by a delicate interplay between chemisorption and physisorption processes. The first-principles simulation of transition metals requires particular care also because they can be viewed as intermediate systems between simple metals and insulating crystals. Even in these cases the method performs well as demonstrated by comparing our results with available experimental data and other theoretical investigations. We confirm that the rare-gas Xe atom is preferentially adsorbed on the top-site configuration on the Ni(111) surface too. Our approach, based on the use of the maximally localized Wannier functions, also allow us to well characterize the bonds between graphene and Ni(111).