In a changing environment, changes in terrestrial water storage (TWS) in basins have a significant impact on potential floods and affect flood risk assessment. Therefore, we aimed to study the impact of TWS on potential floods. In this study, we reconstructed the TWS based on precipitation and temperature, evaluated the reconstructed TWS data based on Gravity Recovery and Climate Experiment (GRACE)-TWS data, and analyzed and calculated the flood potential index (FPI) in the Yangtze River Basin (YRB). The related influencing factors were analyzed based on the Global Land Data Assimilation System (GLDAS) data and Granger’s causality test. The main conclusions are as follows: (1) although the GRACE-TWS anomaly (GRACE-TWSA) in the YRB showed an increasing trend for the averaged TWSA over all grids in the whole basin (i.e., 0.31 cm/a, p < 0.05), the variable infiltration capacity-soil moisture anomalies (VIC-SMA) showed a decreasing trend (i.e., −0.048 cm/a, p > 0.05) during April 2002–December 2019; (2) a larger relative contribution of detrended precipitation to FPI was found in the Jialingjiang River Basin (JRB), Wujiang River Basin (WRB), Dongting Lake Rivers Basin (DLRB), YinBin-Yichang reaches (YB-YC), and Yichang-Hukou reaches (YC-HK), while the contribution of detrended TWS to FPI in the Poyang Lake Rivers Basin (PLRB) was larger than that in other basins; and (3) the original and detrended soil moisture (SM) and TWS in the YRB showed a significant positive correlation (p < 0.05), while the significant effect of SM on TWS caused a change in FPI in the YRB and its sub-basins. This study is of great significance for the correct understanding of the FPI and the accurate assessment of flood risk.