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 C4 photosynthesis as a study system, a derived physiology that increases plant productivity in warm, dry conditions. The grass Alloteropsis semialata includes C4 and non-C4 genotypes, with some populations using laterally acquired C4 -adaptive loci, providing an outstanding system to track the spread of novel adaptive mutations. Using genome data from C4 and non-C4 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 C4 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 C4 functions were rapidly passed between populations with otherwise distinct genomic backgrounds. Thus, our intraspecific study of C4 -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.