The Ashkenazi Jewish (AJ) population is a genetic isolate close to European and Middle Eastern groups, with genetic diversity patterns conducive to disease mapping. Here we report high-depth sequencing of 128 complete genomes of AJ controls. Compared with European samples, our AJ panel has 47% more novel variants per genome and is eightfold more effective at filtering benign variants out of AJ clinical genomes. Our panel improves imputation accuracy for AJ SNP arrays by 28%, and covers at least one haplotype in ≈ 67% of any AJ genome with long, identical-by-descent segments. Reconstruction of recent AJ history from such segments confirms a recent bottleneck of merely ≈ 350 individuals. Modelling of ancient histories for AJ and European populations using their joint allele frequency spectrum determines AJ to be an even admixture of European and likely Middle Eastern origins. We date the split between the two ancestral populations to ≈ 12-25 Kyr, suggesting a predominantly Near Eastern source for the repopulation of Europe after the Last Glacial Maximum.