Topographic and hydro-climatic features of South Korea are highly heterogeneous and able to influence the drought phenomena in the region. The complex topographical and hydro-climatic features of South Korea need a statistically accurate method to find homogeneous regions. Regionalization of drought in a bivariate framework has scarcely been applied in South Korea before. Hierarchical Classification on Principal Components (HCPC) algorithm together with Principal Component Analysis (PCA) method and cluster validation indices were investigated and used for the regionalization of drought across the South Korean region. Statistical homogeneity and discordancy of the region was tested on univariate and bivariate frameworks. HCPC indicate that South Korea should be divided into four regions which are closer to being homogeneous. Univariate and bivariate homogeneity and discordancy tests showed the significant difference in their results due to the inability of univariate homogeneity and discordancy measures to consider the joint behavior of duration and severity. Regionalization of drought for SPI time scale of 1, 3, 6, 12, and 24 months showed significant variation in discordancy and homogeneity of the region with the change in SPI time scale. The results of this study can be used as basic data required to establish a drought mitigation plan on regional scales.