The geographic origin and time of dispersal of Austroasiatic (AA) speakers, presently settled in south and southeast Asia, remains disputed. Two rival hypotheses, both assuming a demic component to the language dispersal, have been proposed. The first of these places the origin of Austroasiatic speakers in southeast Asia with a later dispersal to south Asia during the Neolithic, whereas the second hypothesis advocates pre-Neolithic origins and dispersal of this language family from south Asia. To test the two alternative models, this study combines the analysis of uniparentally inherited markers with 610,000 common single nucleotide polymorphism loci from the nuclear genome. Indian AA speakers have high frequencies of Y chromosome haplogroup O2a; our results show that this haplogroup has significantly higher diversity and coalescent time (17-28 thousand years ago) in southeast Asia, strongly supporting the first of the two hypotheses. Nevertheless, the results of principal component and "structure-like" analyses on autosomal loci also show that the population history of AA speakers in India is more complex, being characterized by two ancestral components - one represented in the pattern of Y chromosomal and EDAR results and the other by mitochondrial DNA diversity and genomic structure. We propose that AA speakers in India today are derived from dispersal from southeast Asia, followed by extensive sex-specific admixture with local Indian populations.