Abstract A time lag exists between precipitation P falling and being converted into terrestrial water. The responses of terrestrial water storage (TWS) and its individual components to P over the global scale, which are vital for understanding the interactions and mechanisms between climatic variables and hydrological components, are not well constrained. In this study, relying on land surface models, we isolate five component storage anomalies from TWS anomalies (TWSA) derived from the Gravity Recovery and Climate Experiment mission (GRACE): canopy water storage anomalies (CWSA), surface water storage anomalies (SWSA), snow water equivalent anomalies (SWEA), soil moisture storage anomalies (SMSA), and groundwater storage anomalies (GWSA). The responses of TWSA and of the individual components of TWSA to P are then evaluated over 168 global basins. The lag between TWSA and P is quantified by calculating the correlation coefficients between GRACE-based TWSA and P for different time lags, then identifying the lag (measured in months) corresponding to the maximum correlation coefficient. A multivariate regression model is used to explore the relationship between climatic and basin characteristics and the lag between TWSA and P. Results show that the spatial distribution of TWSA trend presents a similar global pattern to that of P for the period January 2004–December 2013. TWSA is positively related to P over basins but with lags of variable duration. The lags are shorter in the low- and midlatitude basins (1–2 months) than those in the high-latitude basins (6–9 months). The spatial patterns of the maximum correlations and the corresponding lags between individual components of the TWSA and P are consistent with those of the GRACE-based analysis, except for SWEA (3–8 months) and CWSA (0 months). The lags between GWSA, SMSA, and SWSA to P can be arranged as GWSA > SMSA ≥ SWSA. Regression analysis results show that the lags between TWSA and P are related to the mean temperature, mean precipitation, mean latitude, mean longitude, mean elevation, and mean slope.