Predicting adaptive trajectories is a major goal of evolutionary biology and useful for practical applications. Systems biology has enabled the development of genome-scale metabolic models. However, analysing these models via flux balance analysis (FBA) cannot predict many evolutionary outcomes including adaptive diversification, whereby an ancestral lineage diverges to fill multiple niches. Here we combine in silico evolution with FBA and apply this modelling framework, evoFBA, to a long-term evolution experiment with Escherichia coli. Simulations predicted the adaptive diversification that occurred in one experimental population and generated hypotheses about the mechanisms that promoted coexistence of the diverged lineages. We experimentally tested and, on balance, verified these mechanisms, showing that diversification involved niche construction and character displacement through differential nutrient uptake and altered metabolic regulation. The evoFBA framework represents a promising new way to model biochemical evolution, one that can generate testable predictions about evolutionary and ecosystem-level outcomes.