The Nile River Basin (NRB) has experienced a notable rise in drought episodes in recent decades. The propagation of meteorological, agricultural, and groundwater drought dynamics in the NRB was investigated in this study. The following drought indices examined the correlation and propagation among meteorological, agricultural, and groundwater droughts. These are the standardized precipitation evapotranspiration index (SPEI), soil moisture index, Gravity Recovery and Climate Experiment, and GRACE Follow-On (GRACE/GRACE-FO)-derived groundwater drought index (GGDI). These droughts were comprehensively evaluated in the NRB from 2003 to 2022. The cross-wavelet transform approach highlighted the links between droughts. The following are the key findings: (1) In the NRB, the cross-wavelet energy spectrum of wavelet coherence can indicate the internal connection between meteorological versus (vs.) agricultural and agricultural versus (vs.) groundwater drought. The time scale with the most significant correlation coefficient is the drought propagation time. (2) The El Niño–Southern Oscillation (ENSO) correlated with agricultural and groundwater drought much more than the Indian Ocean Dipole (IOD), demonstrating that ENSO has an important impact on drought advancement. (3) The R2 values were 0.68 for GGDI vs. standardized soil moisture index (SSI), 0.71 for Blue Nile Region (BNR) GGDI vs. SSI, and 0.55 for SSI vs. Standardized Precipitation Evapotranspiration Index (SPEI). Similarly, in the Lake Victoria Region (LVR), GGDI vs. SSI was 0.51 and SSI vs. SPEI was 0.55, but in the Bahr-el-Ghazal Region (BER), GGDI vs. SSI was 0.61 and SSI vs. SPEI was 0.27 during the whole research period with varied lag durations ranging from 1 to 6 months. Thus, the propagation of drought (i.e., meteorological, agricultural, and groundwater drought) dynamics has the potential to reshape our understanding of drought evolution, which could lead to early drought forecasting across the NRB and similar climatic regions.