Drought is a complex climate hazard that is increasing in frequency and severity in parts of the world due to climate change. More research is needed to identify the relationship of drought on human health. In this study, we present a statistical model to evaluate the effect of drought exposure on health outcomes. Specifically, we introduce a Bayesian negative binomial regression model with spatial and temporal variabilities to examine the association between respiratory mortality and drought exposure. To conduct a Bayesian computation, an efficient computational algorithm was developed. The deviance information criteria (DIC) was computed to determine which of three drought indices (USDM, 6-month SPEI, 12-month SPEI) is the most suitable drought indicator. The proposed method is applied to a study of the health effects of drought in two selected states, Arizona and California, from 2000 to 2018.