>Most of our understanding of the genetic basis of human adaptation is biased toward loci of large phenotypic effect. Genome wide association studies (GWAS) now enable the study of genetic adaptation in highly polygenic phenotypes. Here we test for polygenic adaptation among 187 world- wide human populations using polygenic scores constructed from GWAS of 34 complex traits. By comparing these polygenic scores to a null distribution under genetic drift, we identify strong signals of selection for a suite of anthropometric traits including height, infant head circumference (IHC), hip circumference (HIP) and waist-to-hip ratio (WHR), as well as type 2 diabetes (T2D). In addition to the known north-south gradient of polygenic height scores within Europe, we find that natural selection has contributed to a gradient of decreasing polygenic height scores from West to East across Eurasia, and that this gradient is consistent with selection on height in ancient populations who have contributed ancestry broadly across Eurasia. We find that the signal of selection on HIP can largely be explained as a correlated response to selection on height. However, our signals in IHC and WC/WHR cannot, suggesting a response to selection along multiple axes of body shape variation. Our observation that IHC, WC, and WHR polygenic scores follow a strong latitudinal cline in Western Eurasia support the role of natural selection in establishing Bergmann's Rule in humans, and are consistent with thermoregulatory adaptation in response to latitudinal temperature variation.