Recent work comparing historical hydrographic data with modern Argo observations shows a long-term change in the global ocean temperature. The magnitude of this change is greater than estimates of late 20th century warming, and implies a century-scale change in the global oceans. Using global coupled climate models from the Coupled Model Intercomparison Project Phase 5 suite of simulations, we assess to what extent this observed temperature difference can be attributed to a genuine long-term warming trend. After accounting for natural variability and sampling errors, we find convincing evidence that there has indeed been a century-scale anthropogenic warming of the global ocean up to the present day, and a strong possibility of anthropogenic warming from 1873 to 1955. The estimated 1873-1955 ocean warming implies a net top-of-atmosphere energy imbalance of 0.1 ± 0.06 Wm-2, and a thermosteric global mean sea level rise of 0.50 ± 0.2 mma-1.