Ancient DNA (aDNA) has been a revolutionary technology in understanding human history but has not been used extensively to study natural selection as large sample sizes to study allele frequency changes over time have thus far not been available. Here, we examined a time transect of 708 published samples over the past 7,000 years of European history using multi-locus genotype-based selection scans. As aDNA data is affected by high missingness, ascertainment bias, DNA damage, random allele calling, and is unphased, we first validated our selection scan,G12ancient, on simulated data resembling aDNA under a demographic model that captures broad features of the allele frequency spectrum of European genomes as well as positive controls that have been previously identified and functionally validated in modern European datasets on data from ancient individuals from time periods very close to the present time. We then applied our statistic to the aDNA time transect to detect and resolve the timing of natural selection occurring genome wide and found several candidates of selection across the different time periods that had not been picked up by selection scans using single SNP allele frequency approaches. In addition, enrichment analysis discovered multiple categories of complex traits that might be under adaptation across these periods. Our results demonstrate the utility of applying different types of selection scans to aDNA to uncover putative selection signals at loci in the ancient past that might have been masked in modern samples.