Graphene substrates are known to have randomly located functional groups on their surface, particularly at their edges, including carboxylate, carbonyl, epoxy, and alcohol functionalities. However, the detailed interactions of these graphene functionalities with metal oxide nanoclusters are unexplored. This work examined the interaction of titania nanostructures with both graphene and functionalized graphene nanoribbons (GNRs) using density functional theory (DFT) calculations. The interactions of TiO2 (anatase, rutile, and molecular) with graphene were found to favor the physisorption of rutile titania. The interactions of TiO2 with GNRs were found to considerably improve the strength of the nanostructure binding to the substrate with rutile and anatase showing similar chemisorption. Charge density maps showed the importance of the electron distribution in the interaction between titania and graphene with chemisorption sites. Valuable information on the strength of the binding energies was determined by studying the electronic structure using partial density of states (PDOS) of the TiO2/graphene systems at specific adsorption sites. These results show the potential for controlled and oriented growth mechanisms that have applications in next generation photovoltaic and photocatalytic devices.