Ocean mass and thus sea level is significantly affected by water storage on the continents. However, assessing the net contribution of continental water storage change to ocean mass change remains a challenge. We present an integrated version of the WaterGAP global hydrological model that is able to consistently simulate total water storage anomalies (TWSAs) over the global continental area (except Greenland and Antarctica) by integrating the output from the global glacier model of Marzeion et al. (2012) as an input to WaterGAP. Monthly time series of global mean TWSAs obtained with an ensemble of four variants of the integrated model, corresponding to different precipitation input and irrigation water use assumptions, were validated against an ensemble of four TWSA solutions based on the Gravity Recovery and Climate Experiment (GRACE) satellite gravimetry from January 2003 to August 2016. With a mean Nash-Sutcliffe efficiency (NSE) of 0.87, simulated TWSAs fit well to observations. By decomposing the original TWSA signal into its seasonal, linear trend and interannual components, we found that seasonal and interannual variability are almost exclusively caused by the glacier-free land water storage anomalies (LWSAs). Seasonal amplitude and phase are very well reproduced (NSE=0.88). The linear trend is overestimated by 30 %-50 % (NSE=0.65), and interannual variability is captured to a certain extent (NSE=0.57) by the integrated model. During the period 1948-2016, we find that continents lost 34-41 mm of sea level equivalent (SLE) to the oceans, with global glacier mass loss accounting for 81 % of the cumulated mass loss and LWSAs accounting for the remaining 19 %. Over 1948-2016, the mass gain on land from the impoundment of water in artificial reservoirs, equivalent to 8 mm SLE, was offset by the mass loss from water abstractions, amounting to 15-21 mm SLE and reflecting a cumulated groundwater depletion of 13-19 mm SLE. Climate-driven LWSAs are highly sensitive to precipitation input and correlate with El Niño Southern Oscillation multi-year modulations. Significant uncertainty remains in the trends of modelled LWSAs, which are highly sensitive to the simulation of irrigation water use and artificial reservoirs.