Understanding how genetic variants influence disease risk and complex traits (variant-to-function) is one of the major challenges in human genetics. Here we present a model-driven framework to leverage human genome-scale metabolic networks to define how genetic variants affect biochemical reaction fluxes across major human tissues, including skeletal muscle, adipose, liver, brain and heart. As proof of concept, we build personalised organ-specific metabolic flux models for 524,615 individuals of the INTERVAL and UK Biobank cohorts and perform a fluxome-wide association study (FWAS) to identify 4312 associations between personalised flux values and the concentration of metabolites in blood. Furthermore, we apply FWAS to identify 92 metabolic fluxes associated with the risk of developing coronary artery disease, many of which are linked to processes previously described to play in role in the disease. Our work demonstrates that genetically personalised metabolic models can elucidate the downstream effects of genetic variants on biochemical reactions involved in common human diseases.