Drought has become a very frequent hydrological event globally, including in Croatia. It can generally be explained by air temperature and precipitation changes on an annual and seasonal basis, owing to climate change. To contribute to the knowledge on drought phenomena in Croatia, the changes in air temperature and precipitation over a relatively long period between 1951 and 2018 were analyzed. The meteorological stations included in the research were Osijek, Zagreb, and Split, which represented the climate of the entire country. Drought was estimated using the standardized precipitation evapotranspiration index, which is one of the most comprehensive drought indices. Furthermore, the drought severity and duration were calculated using run theory. These parameters were tested for homogeneity using the standard normal homogeneity test. Only the air temperature exhibited inhomogeneity, with a break year in 1991 (Zagreb and Split) and 1998 (Osijek). The existence of significant temporal trends was tested using the non-parametric Mann–Kendall trend test. The probability of drought occurrence with a certain duration and severity was calculated using the copula function. Finally, principal component analysis was applied to the computed standardized Mann–Kendall test statistic (ZMK) to define the relevance of each parameter change and their combination in drought occurrence on a seasonal basis. Drought occurrence was less recognizable from 1951 to 1991 (1998). In the second sub-period, the impact of an increasing air temperature was the most significant variable, particularly in Zagreb.