Background: Logistics plays a key role in economic performance, yet its contribution to global growth and convergence remains underexplored. This study examines how different logistics dimensions have influenced GDP per worker across countries over the period 2007–2022. Methods: Using econometric panel data techniques and convergence models (β and σ), data from 86 countries are analysed by incorporating logistics performance indicators—such as infrastructure quality, customs efficiency, and shipment traceability—into an endogenous growth framework. Results: The analysis confirms the existence of both β- and σ-convergence, suggesting that lower-income countries are catching up with higher-income ones. Improvements in logistics competence and tracking systems positively affect economic growth, while inefficiencies in shipping services and delivery timeliness negatively impact convergence. Conclusions: These findings highlight the dual role logistics can play in fostering or hindering growth. Enhancing logistics infrastructure and services through targeted policies is essential to promote sustained economic development and reduce global income disparities.