Educational attainment (EA) is influenced by characteristics other than cognitive ability, but little is known about the genetic architecture of these "non-cognitive" contributions to EA. Here, we use Genomic Structural Equation Modelling and prior genome-wide association studies (GWASs) of EA (N = 1,131,881) and cognitive test performance (N = 257,841) to estimate SNP associations with EA variation that is independent of cognitive ability. We identified 157 genome-wide significant loci and a polygenic architecture accounting for 57% of genetic variance in EA. Non-cognitive genetics were as strongly related to socioeconomic success and longevity as genetic variants associated with cognitive performance. Noncognitive genetics were further related to openness to experience and other personality traits, less risky behavior, and increased risk for psychiatric disorders. Non-cognitive genetics were enriched in the same brain tissues and cell types as cognitive performance, but showed different associations with gray-matter brain volumes. By conducting a GWAS of a phenotype that was not directly measured, we offer a first view of genetic architecture of non-cognitive skills influencing educational success.