Aim: Rangifer tarandus L. play a key role in Arctic ecosystems as the most numerous and widespread large herbivore. Sea ice is vital for maintaining genetic connectivity in Arctic islands, yet the historical role of sea ice in shaping Rangifer biogeography is unknown. We study the timing of island dispersal and the role of sea ice changes and ice sheet retreat since the last glacial period. Methods: We compiled published datasets of mitochondrial DNA sequences which informed population history scenarios, evaluated in a coalescent-based approximate Bayesian computation (ABC) modelling framework to test hypotheses of island (re)colonisation and to estimate timings of divergence and admixture. Population events were compared with modelled and proxy-based paleo-sea ice cover and published ice sheet chronologies. Results: Our analysis supports Holocene dispersal onto deglaciated Arctic islands rather than High Arctic glacial refugia. The degree of population admixture and the effect of sea ice was dependent on regional geography and climate history. North American initial island population divergence occurred as sea ice cover was declining. A lack of strong genetic structure and late Holocene admixture suggest that island populations were somewhat connected by sea ice during the Holocene. The Svalbard and West Greenland divergence times lagged deglaciation but broadly align with fossil-based estimates of colonisation, suggesting dispersal limitation due to sea ice conditions, potentially modulated by ocean currents and sea ice drift. Main conclusions: Our study sheds light on the Late Quaternary (~60 ka - present) history of Arctic island Rangifer and suggests that ice sheet retreat, sea ice cover, and ocean currents were important in shaping present-day genetic patterns. Regional differences in postglacial dynamics suggest that dispersal during contemporary climate change may vary regionally and depend upon decreasing connectivity provided by sea ice.