We present dispersion-corrected density functional calculations of water and carbon dioxide molecules adsorption on graphene residing on silica and sapphire substrates. The equilibrium positions and bonding distances for the molecules are determined. Water is found to prefer the hollow site in the center of the graphene hexagon, whereas carbon dioxide prefers sites bridging carbon-carbon bonds as well as sites directly on top of carbon atoms. The energy differences between different sites are however minute – typically just a few tenths of a millielectronvolt. Overall, the molecule-graphene bonding distances are found to be in the range 3.1–3.3 Å. The carbon dioxide binding energy to graphene is found to be almost twice that of the water binding energy (around 0.17 eV compared to around 0.09 eV). The present results compare well with previous calculations, where available. Using charge density differences, we also qualitatively illustrate the effect of the different substrates and molecules on the electronic structure of the graphene sheet.