Physiological novelties are often studied at macro-evolutionary scales such that their micro-evolutionary origins remain poorly understood. Here, we test the hypothesis that key components of a complex trait can evolve in isolation and later be combined by gene flow. We use C-4 photosynthesis as a study system, a derived physiology that increases plant productivity in warm, dry conditions. The grass Alloteropsis semialata includes C-4 and non-C-4 genotypes, with some populations using laterally acquired C-4 -adaptive loci, providing an outstanding system to track the spread of novel adaptive mutations. Using genome data from C-4 and non-C-4 A. semialata individuals spanning the species' range, we infer and date past migrations of different parts of the genome. Our results show that photosynthetic types initially diverged in isolated populations, where key C-4 components were acquired. However, rare but recurrent subsequent gene flow allowed the spread of adaptive loci across genetic pools. Indeed, laterally acquired genes for key C-4 functions were rapidly passed between populations with otherwise distinct genomic backgrounds. Thus, our intraspecific study of C-4-related genomic variation indicates that components of adaptive traits can evolve separately and later be combined through secondary gene flow, leading to the assembly and optimization of evolutionary innovations.