The common myna (Acridotheres tristis) is one of the most invasive bird species in the world, yet its colonisation history is only partly understood. We identified the introduction history and population structure, and quantified the genetic diversity of myna populations from the native range in India and introduced populations in New Zealand, Australia, Fiji, Hawaii, and South Africa, based on thousands of single nucleotide polymorphism markers in 814 individuals. We were able to identify the source population of mynas in several invasive locations: mynas from Fiji and Melbourne, Australia, were likely founded by individuals from a subpopulation in Maharashtra, India, while mynas in Hawaii and South Africa were likely independently founded by individuals from other localities in India. Our findings suggest that New Zealand mynas were founded by individuals from Melbourne, which, in turn, were founded by individuals from Maharashtra. We identified two genetic clusters among New Zealand mynas, divided by New Zealand’s North Island’s axial mountain ranges, confirming previous observations that mountains and thick forests may form barriers to myna dispersal. Our study provides a foundation for other population and invasion genomic studies and provides useful information for the management of this invasive species.