The bacterium Shigella sonnei is a major global cause of diarrhoeal disease. This organism has generally been associated with infections in developed countries, but is currently dramatically expanding into industrializing countries. The mechanisms underpinning the spread of S. sonnei are not precisely understood, but we hypothesize that their spread is partly facilitated by resistance to antimicrobials, including the current therapeutic choice to combat Shigella, the fluoroquinolones. To understand how the fluoroquinolone-resistant S. sonnei may become established in a new location, we decoded the total DNA sequences of 71 S. sonnei samples isolated in Bhutan in South Asia between 2011 and 2013. We found that these strains were likely descended from a single isolate that was introduced into Bhutan around 2006. Furthermore, we additionally found that fluoroquinolone resistance emerged prior to the introduction of this founder S. sonnei into Bhutan and these strains then became established, gaining additional genes and resistance to other antimicrobials. Our data describe how drug-resistant S. sonnei may become resident in new locations, and we predict that a similar situation is occurring currently with the epidemic of fluoroquinolone-resistant S. sonnei in Asia and beyond.