Nowadays, the medical systems of the EU Member States have a need for more efficient public policies and strategies to integrate the new societal challenges, the fragile economic recovery from the COVID-19 pandemic, and sustain the development of health systems. This research explores the relationship between public governance and health expenditures allocation, under the theory of welfare economics and the concern for economic development. The research approaches both qualitative and quantitative methodologies. The first refers to bibliometric analysis and review of the existing literature, followed by data mapping process to rank the EU countries based on the variables employed. The quantitative approach also includes advanced empirical analyses (principal component analysis - PCA and regression analysis) performed over the period 2007-2020. Two indices were created through PCA, technical governance and democratic governance, gathering the effects from different world governance indicators. The main results reveal that both governance indices have a direct influence on health expenditures per capita, while GDP growth, applied as a control variable, negatively influences health expenditures. Our results emphasise a need to redesign the public governance of health systems in terms of health spending allocations and increase investments in healthcare to support economic growth in the long run.