The DFT/vdW-WF2s1 method based on the generation of localized Wannier functions, 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 with noble-metal surfaces, namely Ag(111), Au(111), and Cu(111).The study is also repeated by adopting the DFT/vdW-QHO-WF variant relying on the Quantum Harmonic Oscillator model which describes well many-body effects. Comparison of the computed equilibrium binding energies and distances, and the C 3 coefficients characterizing the adatomsurface van der Waals interactions, with available experimental and theoretical reference data shows that the methods perform well and elucidate the importance of properly including screening effects. The results are also compared with those obtained by other vdW-corrected DFT schemes, including PBE-D, vdW-DF, vdW-DF2, rVV10, and by the simpler Local Density Approximation (LDA) and semilocal (PBE) Generalized Gradient Approximation (GGA) approaches.