We present a method for detecting evidence of natural selection in ancient DNA time-series data that leverages an opportunity not utilized in previous scans: testing for a consistent trend in allele frequency change over time. By applying this to 8433 West Eurasians who lived over the past 14000 years and 6510 contemporary people, we find an order of magnitude more genome-wide significant signals than previous studies: 347 independent loci with >99% probability of selection. Previous work showed that classic hard sweeps driving advantageous mutations to fixation have been rare over the broad span of human evolution, but in the last ten millennia, many hundreds of alleles have been affected by strong directional selection. Discoveries include an increase from ∼0% to ∼20% in 4000 years for the major risk factor for celiac disease at HLA-DQB1; a rise from ∼0% to ∼8% in 6000 years of blood type B; and fluctuating selection at the TYK2 tuberculosis risk allele rising from ∼2% to ∼9% from ∼5500 to ∼3000 years ago before dropping to ∼3%. We identify instances of coordinated selection on alleles affecting the same trait, with the polygenic score today predictive of body fat percentage decreasing by around a standard deviation over ten millennia, consistent with the “Thrifty Gene” hypothesis that a genetic predisposition to store energy during food scarcity became disadvantageous after farming. We also identify selection for combinations of alleles that are today associated with lighter skin color, lower risk for schizophrenia and bipolar disease, slower health decline, and increased measures related to cognitive performance (scores on intelligence tests, household income, and years of schooling). These traits are measured in modern industrialized societies, so what phenotypes were adaptive in the past is unclear. We estimate selection coefficients at 9.9 million variants, enabling study of how Darwinian forces couple to allelic effects and shape the genetic architecture of complex traits.