The Roma, also known as 'Gypsies', represent the largest and the most widespread ethnic minority of Europe. There is increasing evidence, based on linguistic, anthropological and genetic data, to suggest that they originated from the Indian subcontinent, with subsequent bottlenecks and undetermined gene flow from/to hosting populations during their diaspora. Further support comes from the presence of Indian uniparentally inherited lineages, such as mitochondrial DNA M and Y-chromosome H haplogroups, in a significant number of Roma individuals. However, the limited resolution of most genetic studies so far, together with the restriction of the samples used, have prevented the detection of other non-Indian founder lineages that might have been present in the proto-Roma population. We performed a high-resolution study of the uniparental genomes of 753 Roma and 984 non-Roma hosting European individuals. Roma groups show lower genetic diversity and high heterogeneity compared with non-Roma samples as a result of lower effective population size and extensive drift, consistent with a series of bottlenecks during their diaspora. We found a set of founder lineages, present in the Roma and virtually absent in the non-Roma, for the maternal (H7, J1b3, J1c1, M18, M35b, M5a1, U3, and X2d) and paternal (I-P259, J-M92, and J-M67) genomes. This lineage classification allows us to identify extensive gene flow from non-Roma to Roma groups, whereas the opposite pattern, although not negligible, is substantially lower (up to 6.3%). Finally, the exact haplotype matching analysis of both uniparental lineages consistently points to a Northwestern origin of the proto-Roma population within the Indian subcontinent.