Temporal variability analysis of rainfall and river discharges is useful in determining the likelihood of the occurrence of extreme events such as drought or flooding for the purposes of developing policies to mitigate their effects. This study investigated the temporal variability of rainfall and discharges into Lake Nakuru, Kenya using meteorological drought indicators and hydrological drought indicators from 1981 to 2018. The standardized precipitation index (SPI) and standardized precipitation evaporation index (SPEI) were used to characterize meteorological drought, while the streamflow drought index (SDI) was used to characterize hydrological drought. A SWAT model was applied for the prediction of streamflow on five tributaries of Lake Nakuru (Njoro, Ngosur, Nderit, Larmudiac, and Makalia Rivers). The model was successfully calibrated on Njoro River at the upstream of river gauging station 2FCO5 from 1984 to 1996, and the parameters were validated from 1997 to 2007. The SUFI-2 algorithm was applied in SWATCup to perform the calibration of the model. The model performance was considered satisfactory in daily time step (NSE = 0.58, R2 = 0.58 during calibration and NSE = 0.52, R2 = 0.68 during validation). The average annual water balance revealed that out of 823 mm received annual precipitation, 154 mm was surface runoff and 178 mm was the annual average water yield. The average annual actual evapotranspiration (ET) was 607 mm. The results for the temporal variation of the SPI and SDI for the five subcatchments indicated that the drought events identified by the 12-month SPI/SPEI were almost all identified by the 12-month SDI. At the catchment scale, SPI showed an equal distribution of wet and dry periods, with 50.00% of positive anomalies and 50.00% of negative anomalies being observed from 1981 to 2018, while SDI observes a high frequency of dry periods (52.63%) and a lower frequency of wet periods (47.37%). There is a higher frequency of wet periods compared to dry periods for both indices from 2009 to 2010 at 60.00% and 40.00% for SPI and 90.00% and 10.00% for SDI, respectively. Both indices observed that 1984 and 2000 were severely dry years (SPI/SPEI < −2.00), while 2018 was severely wet (SPI/SPEI > 2.00). The results for the variability in rainfall and streamflow indices revealed that the last 10 years (2009–2018) were wetter than the period from 1981 to 2008.