In this study, we estimate a time series of geocenter anomalies from a combination of data from the Gravity Recovery and Climate Experiment (GRACE) satellite mission and the output from ocean models. A matrix equation is derived relating total geocenter variations to the GRACE coefficients of degrees two and higher and to the oceanic component of the degree one coefficients. We estimate the oceanic component from t wo state-of-the-art ocean models. Results are compared to independent estimates of geocenter derived from other satellite data, such as satellite laser ranging and GPS. Finally, we compute degree one coefficients that are consistent with the processing applied to the GRACE Level-2 gravity field coefficients. The estimated degree one coefficients can be used to improve estimates of mass variability from GRACE, which alone cannot provide them directly.