The House Crow (Corvus splendens) is a useful study system for investigating the genetic basis of adaptations underpinning successful range expansion. The species originates from the Indian subcontinent, but has successfully spread through a variety of thermal environments across Asia, Africa and Europe. Here, population mitogenomics was used to investigate the colonisation history and to test for signals of molecular selection on the mitochondrial genome. We sequenced the mitogenomes of 89 House Crows spanning four native and five invasive populations. A Bayesian dated phylogeny, based on the 13 mitochondrial protein-coding genes, supports a mid-Pleistocene (~630,000 years ago) divergence between the most distant genetic lineages. Phylogeographic patterns suggest that northern South Asia is the likely centre of origin for the species. Codon-based analyses of selection and assessments of changes in amino acid properties provide evidence of positive selection on the ND2 and ND5 genes against a background of purifying selection across the mitogenome. Protein homology modelling suggests that four amino acid substitutions inferred to be under positive selection may modulate coupling efficiency and proton translocation mediated by OXPHOS complex I. The identified substitutions are found within native House Crow lineages and ecological niche modelling predicts suitable climatic areas for the establishment of crow populations within the invasive range. Mitogenomic patterns in the invasive range of the species are more strongly associated with introduction history than climate. We speculate that invasions of the House Crow have been facilitated by standing genetic variation that accumulated due to diversifying selection within the native range.