The search for a method that utilizes biological information to predict humans' place of origin has occupied scientists for millennia. Over the past four decades, scientists have employed genetic data in an effort to achieve this goal but with limited success. While biogeographical algorithms using next-generation sequencing data have achieved an accuracy of 700km in Europe, they were inaccurate elsewhere. Here we describe the Geographic Population Structure (GPS) algorithm and demonstrate its accuracy with three data sets using 40,000-130,000 SNPs. GPS placed 83% of worldwide individuals in their country of origin. Applied to over 200 Sardinians villagers, GPS placed a quarter of them in their villages and most of the rest within 50km of their villages. GPS's accuracy and power to infer the biogeography of worldwide individuals down to their country or, in some cases, village, of origin, underscores the promise of admixture-based methods for biogeography and has ramifications for genetic ancestry testing.