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Since 2002, the Gravity Recovery and Climate Experiment (GRACE) mission has provided unprecedented observations of global mass redistribution caused by hydrological processes. However, there are still few sources on pre-2002 global terrestrial water storage (TWS). Classical approaches to retrieve past TWS rely on either land surface models (LSMs) or basin-scale water balance calculations. Here we propose a new approach which statistically relates anomalies in atmospheric drivers to monthly GRACE anomalies. Gridded subdecadal TWS changes and time-dependent uncertainty intervals are reconstructed for the period 1985-2015. Comparisons with model results demonstrate the performance and robustness of the derived data set, which represents a new and valuable source for studying subdecadal TWS variability, closing the ocean/land water budgets and assessing GRACE uncertainties. At midpoint between GRACE observations and LSM simulations, the statistical approach provides TWS estimates (doi:10.5905/ethz-1007-85) that are essentially derived from observations and are based on a limited number of transparent model assumptions.