The modelling of drought is of utmost importance for the efficient management of water resources. This article used the adaptive neuro-fuzzy interface system (ANFIS), multilayer perceptron (MLP), radial basis function neural network (RBFNN), and support vector machine (SVM) models to forecast meteorological droughts in Iran. The spatial–temporal pattern of droughts in Iran was also found using recorded observation data from 1980 to 2014. A nomadic people algorithm (NPA) was utilized to train the ANFIS, MLP, RBFNN, and SVM models. Additionally, the NPA was benchmarked against the bat algorithm, salp swarm algorithm, and krill algorithm (KA). The hybrid ANFIS, MLP, RBFNN, and SVM models were used to forecast the 3-month standardized precipitation index. New evolutionary algorithms were utilized to improve the convergence speed of the soft computing models and their accuracy. First, random stations, namely, in Azarbayjan (northwest Iran), Khouzestan (southwest Iran), Khorasan (northeast Iran), and Sistan and Balouchestan (southeast Iran) were selected for the testing of the models. According to the results obtained from the Azarbayjan station, the Nash–Sutcliffe efficiency (NSE) was 0.93, 0.86, 0.85, and 0.83 for the ANFIS–NPA, MLP–NPA, RBFNN–NPA, and SVM–NPA models, respectively. For Sistan and Baloucehstan, the results indicated the superiority of the ANFIS–NPA model, followed by the MLP–NPA model, compared to the RBFNN–NPA and SVM–NPA models, and suggested that the hybrid models performed better than the standalone MLP, RBFNN, ANFIS, and SVM models. The second aim of the study was to capture the relationship between large-scale climate signals and drought indices by using a wavelet coherence analysis. The general results indicated that the NPA and wavelet coherence analysis are useful tools for modelling drought indices.