The language network of the human brain has core components in the inferior frontal cortex and superior/middle temporal cortex, with left-hemisphere dominance in most people. Functional specialization and interconnectivity of these neocortical regions is likely to be reflected in their molecular and cellular profiles. Excitatory connections between cortical regions arise and innervate according to layer-specific patterns. Here we generated a new gene expression dataset from human postmortem cortical tissue samples from core language network regions, using spatial transcriptomics to discriminate gene expression across cortical layers. Integration of these data with existing single-cell expression data identified 56 genes that showed differences in laminar expression profiles between frontal and temporal language cortex together with upregulation in layer II/III and/or layer V/VI excitatory neurons. Based on data from large-scale genome-wide screening in the population, DNA variants within these 56 genes showed set-level associations with inter-individual variation in structural connectivity between left-hemisphere frontal and temporal language cortex, and with predisposition to dyslexia. The axon guidance genes SLIT1 and SLIT2 were consistently implicated. These findings identify region-specific patterns of laminar gene expression as a feature of the brain’s language network.