It is commonly thought that human genetic diversity in non-African populations was shaped primarily by an out-of-Africa dispersal 50–100 thousand yr ago (kya). Here, we present a study of 456 geographically diverse high-coverage Y chromosome sequences, including 299 newly reported samples. Applying ancient DNA calibration, we date the Y-chromosomal most recent common ancestor (MRCA) in Africa at 254 (95% CI 192–307) kya and detect a cluster of major non-African founder haplogroups in a narrow time interval at 47–52 kya, consistent with a rapid initial colonization model of Eurasia and Oceania after the out-of-Africa bottleneck. In contrast to demographic reconstructions based on mtDNA, we infer a second strong bottleneck in Y-chromosome lineages dating to the last 10 ky. We hypothesize that this bottleneck is caused by cultural changes affecting variance of reproductive success among males.