  The OPERA experiment has conclusively observed the appearance of tau
neutrinos in the muon neutrino CNGS beam. Exploiting the OPERA detector
capabilities, it was possible to isolate high purity samples of $\nu_{e}$,
$\nu_{\mu}$ and $\nu_{\tau}$ charged current weak neutrino interactions, as
well as neutral current weak interactions. In this Letter, the full dataset is
used for the first time to test the three-flavor neutrino oscillation model and
to derive constraints on the existence of a light sterile neutrino within the
framework of the $3+1$ neutrino model. For the first time, tau and electron
neutrino appearance channels are jointly used to test the sterile neutrino
hypothesis. A significant fraction of the sterile neutrino parameter space
allowed by LSND and MiniBooNE experiments is excluded at 90% C.L. In
particular, the best-fit values obtained by MiniBooNE combining neutrino and
antineutrino data are excluded at 3.3 $\sigma$ significance.
