The Central and Eastern European countries have made considerable economic progress since the capitalist transformation. This paper investigates whether there is a co-movement between two factors of well-being, improvement of economic and health status between 1995 and 2018 compared to the six founding European Union (EU) member states. Applying the Pedroni- and Fisher-type cointegration test and a panel vector error correction model, our estimations suggest that there is a mutual causal relationship between economic convergence measured in GDP per capita and health status convergence measured by life expectancy. The long-term bi-directional effects are also proved by impulse response functions. Using the same econometric methods, the examination of the relationship between government health expenditure and life expectancy indicates that governmental health expenditure promotes the health status convergence. This study concludes that the FDI-based, low-wage growth model of the Central and Eastern European countries has not impeded the convergence in both factors of well-being to the founding EU member states. The results demonstrate that the improvement of the healthcare system may be a channel for the acceleration of convergence.