A core question in evolutionary biology is whether convergent phenotypic evolution is driven by convergent molecular changes in proteins or regulatory regions. We combined phylogenomic, developmental, and epigenomic analysis of 11 new genomes of paleognathous birds, including an extinct moa, to show that convergent evolution of regulatory regions, more so than protein-coding genes, is prevalent among developmental pathways associated with independent losses of flight. A Bayesian analysis of 284,001 conserved noncoding elements, 60,665 of which are corroborated as enhancers by open chromatin states during development, identified 2355 independent accelerations along lineages of flightless paleognaths, with functional consequences for driving gene expression in the developing forelimb. Our results suggest that the genomic landscape associated with morphological convergence in ratites has a substantial shared regulatory component.