Drought is a detrimental global warming effect that severely impacts the environment, society, and economy. Drought indices are used worldwide for drought monitoring and assessments. This study aims to develop a new meteorological drought index based on fuzzy logic (FL) and neuro-fuzzy models to describe and predict droughts. The developed models were compared to nine conventional drought indices and correlated with multiple drought indicators. Different combinations of inputs (such as maximum temperature, mean temperature, precipitation, and potential evapotranspiration) were tested to develop the models. Observed weather data from Alice Springs, Australia, were used to examine the developed models and train the adaptive neuro-fuzzy inference system (ANFIS) model. Additionally, historical records of various drought indicators were used to evaluate the predictions of all models, including deep soil moisture, lower soil moisture, root zone soil moisture, upper soil moisture, and runoff. This study showed that the rainfall anomaly drought index (RAI) was the best conventional drought index, with the highest correlation (0.718) between the drought index and upper soil moisture (drought indicator). The average of the best-performing FL models outperformed all conventional indices, with a correlation of 0.784 with the upper soil moisture. Moreover, when the average output of the best-performing FL models was used for training, the best ANFIS model had a correlation of 0.809 with upper soil moisture. The best ANFIS model in terms of correlation with conventional drought indices had a correlation of 0.941 with the RAI when the normalised average output of the best-performing conventional drought indices was used for training. To validate the developed models, drought assessment was conducted for five stations in different climate zones and seasons. The validation results showed that the developed models had similar performance to the best-correlated conventional drought index (RAI) in most cases. The developed models yielded better predictions compared to the conventional index in the subtropical and tropical regions. Overall, the developed soft computing drought indices based on fuzzy logic and ANFIS outperformed conventional methods, thus effectively contributing to more precise drought prediction and mitigation.