First-principles DFT calculations are carried out to study the changes in structures and electronic properties of two-dimensional single-layer graphene in the presence of non-covalent interactions induced by carbon and boron fullerenes (C60, C70, C80 and B80). Our study shows that larger carbon fullerene interacts more strongly than the smaller fullerene, and boron fullerene interacts more strongly than that of its carbon analogue with the same nuclearity. We find that van der Waals interactions play a major role in governing non-covalent interactions between the adsorbed fullerenes and graphene. Moreover, a greater extent of van der Waals interactions found for the larger fullerenes, C80 and B80, relative to smaller C60, and consequently, results in higher stabilisation. We find a small amount of electron transfer from graphene to fullerene, which gives rise to a hole-doped material. We also find changes in the graphene electronic band structures in the presence of these surface-decorated fullerenes. The Dirac cone picture, such as that found in pristine graphene, is significantly modified due to the re-hybridisation of graphene carbon orbitals with fullerenes orbitals near the Fermi energy. However, all of the composites exhibit perfect conducting behaviour. The simulated absorption spectra for all of the graphene–fullerene hybrids do not exhibit a significant change in the absorption peak positions with respect to the pristine graphene absorption spectrum. Additionally, we find that the hole-transfer integral between graphene and C60 is larger than the electron-transfer integrals and the extent of these transfer integrals can be significantly tuned by graphene edge functionalisation with carboxylic acid groups. Our understanding of the non-covalent functionalisation of graphene with various fullerenes would promote experimentalists to explore these systems, for their possible applications in electronic and opto-electronic devices.