The provenance and age of two Homo sapiens fossils (Omo I and Omo II) from the Kibish Formation in southern Ethiopia have been much debated. Here we confirm that Omo I and the somewhat more primitive-looking Omo II calvariae are from similar stratigraphic levels in Member I of the Kibish Formation. Based on (40)Ar/(39)Ar age measurements on alkali feldspar crystals from pumice clasts in the Nakaa'kire Tuff, a tuffaceous bed in Member I just below the hominin levels, we place an older limit of 198+/-14 ka (weighted mean age=196+/-2 ka) for the hominins. A younger limit of 104+/-7 ka (weighted mean age=104+/-1 ka) is provided by feldspars separated from pumice clasts in the Aliyo Tuff in Member III. Geological evidence indicates rapid deposition of each member of the Kibish Formation, concurrent with deposition of sapropels in the Mediterranean Sea. The (40)Ar/(39)Ar age measurements, together with correlations with sapropels, indicate that the hominin fossils are close in age to the older limit. Our preferred estimate of the age of the hominins is 195+/-5 ka, making them the earliest well-dated anatomically modern humans yet described.