BV GWAS meta-analysis of 47,316 Europeans identifies 18 loci and 343 genes. SNP heritability of BV is 21.4%. Genetic correlation between BV and intelligence is 0.24. 92 genes overlap between BV and intelligence, mainly in cell growth signaling pathways. Mendelian randomization shows BV causally increases intelligence. Intelligence also causally increases BV bidirectionally. 32 prioritized shared genes likely drive functional impact. BV genes enriched in conserved regions and transcription start sites. BV positively genetically correlates with education, BMI, and birth weight. BV negatively genetically correlates with ADHD, neuroticism, and insomnia. 14 BV loci and 270 genes novel. Shared genes more intolerant to loss-of-function mutations. Shared genes enriched for developmental disorders. BV genes linked to monogenic brain size disorders like microcephaly. No sex differences in BV-intelligence relation. Phenotypic BV-intelligence correlation is 0.24 after bias correction. Sign concordance of BV lead variants in intelligence is 100%. Overlapping genes not region-specific in cortex. Gene sets for BV and intelligence are trait-specific.