Convergent evolution can occur through different genetic mechanisms in different species. It is now clear that convergence at the genetic level is also widespread, and can be caused by either i) parallel genetic evolution, where independently evolved convergent mutations arise in different populations or species, or ii) collateral evolution in which shared ancestry results from either ancestral polymorphism or introgression among taxa. The adaptive radiation of Heliconius butterflies shows colour pattern variation within species, as well as mimetic convergence between species. Using comparisons from across multiple hybrid zones, we use signals of shared ancestry to identify and refine multiple putative regulatory elements in Heliconius melpomene and its co-mimics, Heliconius elevatus and Heliconius besckei, around three known major colour patterning genes optix, WntA and cortex While we find that convergence between H. melpomene and H. elevatus is caused by a complex history of collateral evolution via introgression in the Amazon, convergence between these species in the Guianas appears to have evolved independently. Thus, we find adaptive convergent genetic evolution to be a key driver of regulatory changes that lead to rapid phenotypic changes. Furthermore, we uncover evidence of parallel genetic evolution at some loci around optix and WntA in H. melpomene and its distant co-mimic Heliconius erato. Ultimately, we show that all three of convergence, conservation, and novelty underlie the modular architecture of Heliconius colour pattern mimicry.