This paper reports on the first observation of electroweak production of single top quarks by the DZero and CDF collaborations. At Fermilabs 1.96 TeV proton-antiproton collider, a few thousand events are selected from several inverse femtobarns of data that contain an isolated electron or muon and/or missing transverse energy, together with jets that originate from the decays of b quarks. Using sophisticated multivariate analyses to separate signal from background, the DZero collaboration measures a cross section sigma(ppbar->tb+X,tqb+X) = 3.94 +- 0.88 pb (for a top quark mass of 170 GeV) and the CDF collaboration measures a value of 2.3_0.6 -0.5 pb (for a top quark mass of 175 GeV). These values are consistent with theoretical predictions at next-to-leading order precision. Both measurements have a significance of 5.0 standard deviations, meeting the benchmark to be considered unambiguous observation.