This article shows that the spin-to-charge current conversion in single-layer graphene (SLG) by means of the inverse Rashba-Edelstein effect (IREE) is made possible with the integration of this remarkable 2D-material with the unique ferrimagnetic insulator yttrium iron garnet (YIG = Y3Fe5O12) as well as with the ferromagnetic metal permalloy (Py = Ni81Fe19). By means of X-ray absorption spectroscopy (XAS) and magnetic circular dichroism (XMCD) techniques, we show that the carbon atoms of the SLG acquires an induced magnetic moment due to the proximity effect with the magnetic layer. The spin currents are generated in the magnetic layer by spin pumping from microwave driven ferromagnetic resonance and are detected by a dc voltage along the graphene layer, at room temperature. The spin-to-charge current conversion, occurring at the graphene layer, is explained by the extrinsic spin-orbit interaction (SOI) induced by the proximity effect with the ferromagnetic layer. The results obtained for the SLG/YIG and SLG/Py systems confirm very similar values for the IREE parameter, which are larger than the values reported in previous studies for SLG. We also report systematic investigations of the electronic and magnetic properties of the SLG/YIG by means of scanning tunneling microscopy (STM).