Under the variable climatic conditions, the conventional Standardized Precipitation Index (SPI) and Reconnaissance Drought Index (RDI) are inadequate for predicting extreme drought characteristics. So in the present study, two indices namely, Non-stationary Standardized Precipitation Index (NSPI) and Non-stationary Reconnaissance Drought Index (NRDI) are developed by fitting non-stationary gamma (for precipitation series) and lognormal (for initial values,δ0) distributions. The Generalized Additive Model in Location, Scale and Shape (GAMLSS) framework, with time varying location parameters considering the external covariates, is used to fit the non-stationary distributions. This includes various large scale climate indices namely Multivariate ENSO Index (MEI), Southern Oscillation Index (SOI), Sea Surface Temperature (SST), and Indian Ocean Dipole (IOD) as external covariates for the non-stationary drought assessment. The performances of stationary and non-stationary models are compared based on the Akaika Information Criterion (AIC). Additionally, the drought characteristics are evaluated using Run theory analysis for both stationary and non-stationary drought indices. The study also concentrated on the trivariate copula as well as the Pairwise Copula Construction (PCC) models to estimate the drought recurrence intervals. The comparison of two copula models revealed that the PCC model performed better than the trivariate Student’s t copula model. The recurrence intervals arrived at for the drought events are different for trivariate copula model and PCC model. The area taken for the study is the Upper and Lower sub basins of the Godavari River basin. This study shows that non-stationary drought indices will be helpful in the accurate estimate of the drought characteristics under the changing climatic scenario.