To develop a quantitative theory that can predict how microbiomes assemble, and how they respond to perturbations, we must identify which descriptive features of microbial communities are reproducible and predictable, which are unpredictable, and why. The emergent metagenomic structure of communities is often quantitatively convergent in similar habitats, with highly similar fractions of the metagenome being devoted to the same metabolic pathways. By contrast, the species-level taxonomic composition is often highly variable even in replicate environments. The mechanisms behind these patterns are not yet understood. By studying the self-assembly of hundreds of communities in replicate, synthetic habitats, we show that the reproducibility of microbial community assembly reflects an emergent metabolic structure, which is quantitatively predictable from first-principles, genome-scale metabolic models. Taxonomic variability within functional groups arises through multistability in population dynamics, and the species-level community composition is predictably governed by the mutual competitive exclusion of two sub-dominant strains. Our findings provide a mechanistic bridge between microbial community structure at different levels of organization, and show that the evolutionary conservation of metabolic traits, both in terms of growth responses and niches constructed, can be leveraged to quantitatively predict the taxonomic and metabolic structure of microbial communities.