Theory predicts that in allopatric populations, genomic divergence and reproductive barriers will evolve slowly under random genetic drift. However, the degree of local adaptation, divergence under selection and reproductive isolation in allopatric populations itself has been poorly characterised. Here we address three key questions in young allopatric species: (a) How widespread are the genomic signatures of adaptative divergence?, (b) What is the functional space along which young sister species show divergence at the genomic level?, and (c) How quickly might pre-zygotic and post-zygotic reproductive barriers evolve? Analysis of 82 genomes of the Oriental Papilio polytes species group containing five well-defined allopatric species revealed surprisingly widespread hotspots of intense selection and selective sweeps at hundreds of genes unique to each species, and spanning all chromosomes. These genes occupy a diverse functional space such as wing development, colour patterning, courtship behaviour, mimicry, pheromone synthesis and olfaction, and host plant use and digestion of secondary metabolites, that usually contribute to reproductive isolation and local adaptation. In behavioural and hybridisation experiments these species also showed strong assortative mate preference and other prezygotic and postzygotic barriers to hybridisation in timespans as short as 1.27 my. Our study thus demonstrates strong reproductive isolation and unusually rapid genome-wide divergence in young allopatric species. It points to a previously unappreciated role of intense selection and local adaptation in creating genome-wide hotspots of rapid molecular evolution and divergence, rather than divergence predominantly under drift or divergence only in a few genomic islands, during allopatric differentiation and speciation.