It is well established that higher cognitive ability is associated with larger brain size. However, individual variation in intelligence exists despite brain size and recent studies have shown that a simple unifactorial view of the neurobiology underpinning cognitive ability is probably unrealistic. Educational attainment (EA) is often used as a proxy for cognitive ability since it is easily measured, resulting in large sample sizes and, consequently, sufficient statistical power to detect small associations. This study investigates the association between three global (total surface area (TSA), intra-cranial volume (ICV) and average cortical thickness) and 34 regional cortical measures with educational attainment using a polygenic scoring (PGS) approach. Analyses were conducted on two independent target samples of young twin adults with neuroimaging data, from Australia (N ​= ​1097) and the USA (N ​= ​723), and found that higher EA-PGS were significantly associated with larger global brain size measures, ICV and TSA (R2 ​= ​0.006 and 0.016 respectively, p ​< ​0.001) but not average thickness. At the regional level, we identified seven cortical regions—in the frontal and temporal lobes—that showed variation in surface area and average cortical thickness over-and-above the global effect. These regions have been robustly implicated in language, memory, visual recognition and cognitive processing. Additionally, we demonstrate that these identified brain regions partly mediate the association between EA-PGS and cognitive test performance. Altogether, these findings advance our understanding of the neurobiology that underpins educational attainment and cognitive ability, providing focus points for future research.