Genetic and fossil evidence supports a single, recent (<200,000 yr) origin of modern Homo sapiens in Africa, followed by later population divergence and dispersal across the globe (the "Out of Africa" model). However, there is less agreement on the exact nature of this migration event and dispersal of populations relative to one another. We use the empirically observed genetic correlation structure (or linkage disequilibrium) between 242,000 genome-wide single nucleotide polymorphisms (SNPs) in 17 global populations to reconstruct two key parameters of human evolution: effective population size (N(e)) and population divergence times (T). A linkage disequilibrium (LD)-based approach allows changes in human population size to be traced over time and reveals a substantial reduction in N(e) accompanying the "Out of Africa" exodus as well as the dramatic re-expansion of non-Africans as they spread across the globe. Secondly, two parallel estimates of population divergence times provide clear evidence of population dispersal patterns "Out of Africa" and subsequent dispersal of proto-European and proto-East Asian populations. Estimates of divergence times between European-African and East Asian-African populations are inconsistent with its simplest manifestation: a single dispersal from the continent followed by a split into Western and Eastern Eurasian branches. Rather, population divergence times are consistent with substantial ancient gene flow to the proto-European population after its divergence with proto-East Asians, suggesting distinct, early dispersals of modern H. sapiens from Africa. We use simulated genetic polymorphism data to demonstrate the validity of our conclusions against alternative population demographic scenarios.