Theoretical estimates indicate that graphene thin films can be used as transparent electrodes for thin-film devices such as solar cells and organic light-emitting diodes, with an unmatched combination of sheet resistance and transparency. We demonstrate organic light-emitting diodes with solution-processed graphene thin film transparent conductive anodes. The graphene electrodes were deposited on quartz substrates by spin-coating of an aqueous dispersion of functionalized graphene, followed by a vacuum anneal step to reduce the sheet resistance. Small molecular weight organic materials and a metal cathode were directly deposited on the graphene anodes, resulting in devices with a performance comparable to control devices on indium-tin-oxide transparent anodes. The outcoupling efficiency of devices on graphene and indium-tin-oxide is nearly identical, in agreement with model predictions.