In 1967 the Kibish Formation in southern Ethiopia yielded hominid cranial remains identified as early anatomically modern humans, assigned to Homo sapiens. However, the provenance and age of the fossils have been much debated. Here we confirm that the Omo I and Omo II hominid fossils are from similar stratigraphic levels in Member I of the Kibish Formation, despite the view that Omo I is more modern in appearance than Omo II. 40Ar/39Ar ages on feldspar crystals from pumice clasts within a tuff in Member I below the hominid levels place an older limit of 198 +/- 14kyr (weighted mean age 196 +/- 2kyr) on the hominids. A younger age limit of 104 +/- 7kyr is provided by feldspars from pumice clasts in a Member III tuff. Geological evidence indicates rapid deposition of each member of the Kibish Formation. Isotopic ages on the Kibish Formation correspond to ages of Mediterranean sapropels, which reflect increased flow of the Nile River, and necessarily increased flow of the Omo River. Thus the 40Ar/39Ar age measurements, together with the sapropel correlations, indicate that the hominid fossils have an age close to the older limit. Our preferred estimate of the age of the Kibish hominids is 195 +/- 5kyr, making them the earliest well-dated anatomically modern humans yet described.