The aim of this study is to investigate the effect of health expenditures on economic growth in the period 2000–2019 in 27 European Union (EU) countries. First, the causality relationship between the variables was analyzed using the panel Fourier Toda–Yamamoto Causality test. The findings demonstrate a bidirectional causality relationship between health expenditures and economic growth on a panel basis. Secondly, the effects of health expenditures on economic growth were examined using the Random Forest Method for the panel and then for each country. According to the Random Forest Method, health expenditures positively affected economic growth, but on the country basis, the effect was different. Then, government health expenditures, private health expenditures, and out-of-pocket expenditures were used, and these three variables were ranked in order of importance in terms of their effects on growth using the Random Forest Method. Accordingly, government health expenditures were the most important variable for economic growth. Finally, Support Vector Regression, Gaussian Process Regression, and Decision Tree Regression models were designed for the simulation of the data used in this study, and the performances of the designed models were analyzed.