The question of Jewish ancestry has been the subject of controversy for over two centuries and has yet to be resolved. The "Rhineland hypothesis" depicts Eastern European Jews as a "population isolate" that emerged from a small group of German Jews who migrated eastward and expanded rapidly. Alternatively, the "Khazarian hypothesis" suggests that Eastern European Jews descended from the Khazars, an amalgam of Turkic clans that settled the Caucasus in the early centuries CE and converted to Judaism in the 8th century. Mesopotamian and Greco-Roman Jews continuously reinforced the Judaized empire until the 13th century. Following the collapse of their empire, the Judeo-Khazars fled to Eastern Europe. The rise of European Jewry is therefore explained by the contribution of the Judeo-Khazars. Thus far, however, the Khazars' contribution has been estimated only empirically, as the absence of genome-wide data from Caucasus populations precluded testing the Khazarian hypothesis. Recent sequencing of modern Caucasus populations prompted us to revisit the Khazarian hypothesis and compare it with the Rhineland hypothesis. We applied a wide range of population genetic analyses to compare these two hypotheses. Our findings support the Khazarian hypothesis and portray the European Jewish genome as a mosaic of Near Eastern-Caucasus, European, and Semitic ancestries, thereby consolidating previous contradictory reports of Jewish ancestry. We further describe a major difference among Caucasus populations explained by the early presence of Judeans in the Southern and Central Caucasus. Our results have important implications for the demographic forces that shaped the genetic diversity in the Caucasus and for medical studies.