The results of the research of a composite based on multi-walled carbon nanotubes (MWCNTs) decorated with CuO/Cu2O/Cu nanoparticles deposited by the cupric formate pyrolysis are discussed. The study used a complementary set of methods, including scanning and transmission electron microscopy, X-ray diffractometry, Raman, and ultrasoft X-ray spectroscopy. The investigation results show the good adhesion between the copper nanoparticles coating and the MWCNT surface through the oxygen atom bridge formation between the carbon atoms of the MWCNT outer graphene layer and the oxygen atoms of CuO and Cu2O oxides. The formation of the Cu–O–C bond between the coating layer and the outer nanotube surface is clearly confirmed by the results of the O 1s near edge X-ray absorption fine structure (NEXAFS) and X-ray photoelectron spectroscopy (XPS) of the Cu/MWCNTs nanocomposite. The XPS measurements were performed using a laboratory spectrometer with sample charge compensation, and the NEXAFS studies were carried out using the synchrotron radiation of the Russian–German dipole beamline at BESSY-II (Berlin, Germany) and the NanoPES station at the Kurchatov Center for Synchrotron Radiation and Nanotechnology (Moscow, Russia).