This paper examines the impact of knowledge assets—technological and human capital—on the regional productivity levels within a Cobb–Douglas production function model, which includes the traditional tangible inputs, as well as other territorial and industrial features of the regions. Spatial panel econometric techniques are applied to account for geographical association and to examine the role of knowledge spillovers from the neighbouring regions. We apply our empirical model to a large set of regions belonging to the EU27 plus Norway and Switzerland over the period 2000–2008. Our main results, robust to a wide array of sensitivity checks, show that both knowledge assets exert a positive impact on gross domestic product, with human capital being more effective than technological capital in most cases. Moreover, we find evidence of spatial spillovers directly associated with the two knowledge assets, which turn out to have a larger effect in the regions of the 12 new accession countries. These results underline the central role played by highly educated labour forces in allowing a region to absorb the potential knowledge spilling from the external territories, especially in developing countries, and to ensure its effective use in the production process.