Convergent evolution is the independent evolution of similar traits in different species or lineages of the same species; this often is a result of adaptation to similar environments, a process referred to as convergent adaptation. We investigate here the molecular basis of convergent adaptation in maize to highland climates in Mesoamerica and South America, using genome-wide SNP data. Taking advantage of archaeological data on the arrival of maize to the highlands, we infer demographic models for both populations, identifying evidence of a strong bottleneck and rapid expansion in South America. We use these models to then identify loci showing an excess of differentiation as a means of identifying putative targets of natural selection and compare our results to expectations from recently developed theory on convergent adaptation. Consistent with predictions across a wide parameter space, we see limited evidence for convergent evolution at the nucleotide level in spite of strong similarities in overall phenotypes. Instead, we show that selection appears to have predominantly acted on standing genetic variation and that introgression from wild teosinte populations appears to have played a role in highland adaptation in Mexican maize.