Super-Kamiokande atmospheric neutrino data were fit with an unbinned maximum likelihood method to search for the appearance of tau leptons resulting from the interactions of oscillation-generated tau neutrinos in the detector. Relative to the expectation of unity, the tau normalization is found to be 1.42 ± 0.35(stat)(-0.12)(+0.14)(syst) excluding the no-tau-appearance hypothesis, for which the normalization would be zero, at the 3.8σ level. We estimate that 180.1 ± 44.3(stat)(-15.2)(+17.8) (syst) tau leptons were produced in the 22.5 kton fiducial volume of the detector by tau neutrinos during the 2806 day running period. In future analyses, this large sample of selected tau events will allow the study of charged current tau neutrino interaction physics with oscillation produced tau neutrinos.