The progression of chronic liver disease to hepatocellular carcinoma is caused by the acquisition of somatic mutations that affect 20-30 cancer genes1-8. Burdens of somatic mutations are higher and clonal expansions larger in chronic liver disease9-13 than in normal liver13-16, which enables positive selection to shape the genomic landscape9-13. Here we analysed somatic mutations from 1,590 genomes across 34 liver samples, including healthy controls, alcohol-related liver disease and non-alcoholic fatty liver disease. Seven of the 29 patients with liver disease had mutations in FOXO1, the major transcription factor in insulin signalling. These mutations affected a single hotspot within the gene, impairing the insulin-mediated nuclear export of FOXO1. Notably, six of the seven patients with FOXO1S22W hotspot mutations showed convergent evolution, with variants acquired independently by up to nine distinct hepatocyte clones per patient. CIDEB, which regulates lipid droplet metabolism in hepatocytes17-19, and GPAM, which produces storage triacylglycerol from free fatty acids20,21, also had a significant excess of mutations. We again observed frequent convergent evolution: up to fourteen independent clones per patient with CIDEB mutations and up to seven clones per patient with GPAM mutations. Mutations in metabolism genes were distributed across multiple anatomical segments of the liver, increased clone size and were seen in both alcohol-related liver disease and non-alcoholic fatty liver disease, but rarely in hepatocellular carcinoma. Master regulators of metabolic pathways are a frequent target of convergent somatic mutation in alcohol-related and non-alcoholic fatty liver disease.