Mixed microbial communities exhibit emergent biochemical properties not found in clonal monocultures. We report a new type of synthetic genetic interaction, synthetic mutualism in trans (SMIT), in which certain pairs of auxotrophic Escherichia coli mutants complement one another's growth by cross-feeding essential metabolites. We find significant metabolic synergy in 17% of 1035 such pairs tested, with SMIT partners identified throughout the metabolic network. Cooperative phenotypes show more growth on average by aiding the proliferation of their conjugate partner, thereby expanding the source of their own essential metabolites. We construct a quantitative, predictive, framework for describing SMIT interactions as governed by stoichiometric models of the metabolic networks of the interacting strains.