A search for lepton flavor violating decays of the 125 GeV Higgs boson in the $\mu\tau$ and $\textrm{e}\tau$ decay modes is presented. The search is based on a dataset of 35.9~\mathrm{fb}^{-1} of proton-proton collisions collected with the CMS detector in 2016, at a center-of-mass energy of 13~\mathrm{TeV}. The tau leptons are reconstructed in the leptonic and hadronic decay modes. No significant excess over the standard model background expectation is observed. The observed (expected) upper limits on the branching fraction of the Higgs boson are found to be $\mathcal{B}(\textrm{H}\rightarrow\mu\tau)<0.25(0.25)\%$ and $\mathcal{B}(\textrm{H}\rightarrow\textrm{e}\tau)<0.61(0.37)\%$ at 95$\%$ confidence level. These results are used to derive upper limits on the off-diagonal $\mu\tau$ and $\textrm{e}\tau$ Yukawa couplings, $\sqrt{|{Y_{\mu\tau}}|^{2}+|{Y_{\tau\mu}}|^{2}}<1.43\times 10^{-3}$ and $\sqrt{|{Y_{\textrm{e}\tau}}|^{2}+|{Y_{\tau\textrm{e}}}|^{2}}<2.26\times 10^{-3}$ at 95$\%$ CL.

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