Accurate estimation of drought events is vital for the mitigation of their adverse consequences on water resources, agriculture and ecosystems. Machine learning algorithms are promising methods for drought prediction as they require less time, minimal inputs, and are relatively less complex than dynamic or physical models. In this study, a combination of machine learning with the Standardized Precipitation Evapotranspiration Index (SPEI) is proposed for analysis of drought within a representative case study in the Tibetan Plateau, China, for the period of 1980-2019. Two timescales of 3 months (SPEI-3) and 6 months (SPEI-6) aggregation were considered. Four machine learning models of Random Forest (RF), the Extreme Gradient Boost (XGB), the Convolutional neural network (CNN) and the Long-term short memory (LSTM) were developed for the estimation of the SPEIs. Seven scenarios of various combinations of climate variables as input were adopted to build the models. The best models were XGB with scenario 5 (precipitation, average temperature, minimum temperature, maximum temperature, wind speed and relative humidity) and RF with scenario 6 (precipitation, average temperature, minimum temperature, maximum temperature, wind speed, relative humidity and sunshine) for estimating SPEI-3. LSTM with scenario 4 (precipitation, average temperature, minimum temperature, maximum temperature, wind speed) was relatively better for SPEI-6 estimation. The best model for SPEI-6 was XGB with scenario 5 and RF with scenario 7 (all input climate variables, i.e., scenario 6 + solar radiation). Based on the NSE index, the performances of XGB and RF models are classified as good fits for scenarios 4 to 7 for both timescales. The developed models produced satisfactory results and they could be used as a rapid tool for decision making by water-managers.