This study assessed the meteorological and hydrological droughts and their relationship over 30 years from 1985 to 2015 in the largest river basin (Mahaweli River Basin (MRB)) in Sri Lanka. Data from 14 rainfall, 5 temperature, and 5 streamflow stations in and near the MRB were used in the present study. Universal drought indices including Standardized Precipitation Index (SPI) and Standardized Precipitation–Evapotranspiration Index (SPEI) were used to assess meteorological droughts. The Standardized Streamflow Index (SSI) was used in investigating hydrological droughts. Correlations between meteorological and hydrological droughts were obtained, annual variations were observed (in terms of SPI, SPEI, and SSI), and the spatial distributions of selected drought events were analyzed. Our results revealed that the highest correlation was found in long-term dry conditions in the wet zone. In addition, some negative correlations found showed the opposite behavior of correlations. Furthermore, in annual variations of droughts, extreme droughts were recorded in the dry zone as maximum values, while results were more prominent in the wet zone. In addition, the spatial distribution performed using SPI, SPEI, and SSI showed an extremely dry condition in 2004. Our findings are beneficial for policymaking and for the decision-makers in assessing meteorological and hydrological drought risks in the future.