A serious natural disaster that poses a threat to people and their living spaces is drought, which is difficult to notice at first and can quickly spread to wide areas through subtle progression. Numerous methods are being explored to identify, prevent, and mitigate drought, and distinct metrics have been developed. In order to contribute to the research on measures to be taken against drought, the Standard Precipitation Evaporation Index (SPEI), one of the drought indices that has been developed and accepted in recent years and includes a more comprehensive drought definition, was chosen in this study. Machine learning and deep learning algorithms, including support vector machine (SVM), random forest (RF), long short-term memory (LSTM), and Gaussian process regression (GPR), were used to model the droughts in six regions of Norway: Bodø, Karasjok, Oslo, Tromsø, Trondheim, and Vadsø. Four distinct model architectures were employed for this goal, and as a novel approach, the models’ output was enhanced by using discrete wavelet decomposition/transformation (WT). The model outputs were evaluated using the correlation coefficient (r), Nash–Sutcliffe efficiency (NSE), and root mean square error (RMSE) as performance evaluation criteria. When the findings were analyzed, the GPR model (W-GPR), which was acquired after WT, typically produced the best results. Furthermore, it was discovered that, out of all the recognized models, M04 had the most effective model structure. Consequently, the most successful outcomes were obtained with W-SVM-M04 for Bodø and W-GPR-M04 for Karasjok, Oslo, Tromsø, Trondheim, and Vadsø. Furthermore, W-GPR-M04 in the Oslo region had the best results across all regions (r: 0.9983, NSE: 0.9966 and RMSE:0.0539).