A search is presented for lepton-flavor violating decays of the Higgs boson to $\mu\tau$ and $e\tau$. The analysis is based on data corresponding to an integrated luminosity of 137~\mathrm{fb}^{-1}, collected at the CMS detector of the LHC in proton-proton collisions at a center-of-mass energy of 13~\mathrm{TeV}. No significant excess has been found, and the results are interpreted in terms of upper limits on lepton-flavor violating branching fractions of the Higgs boson. The observed and expected upper limits on the branching fractions are, respectively, $\mathcal{B}(\mathrm{H}\to\mu\tau)<0.15\%$ and $<0.15\%$ and $\mathcal{B}(\mathrm{H}\to e\tau)<0.22\%$ and $<0.16\%$ set at $95\%$ confidence level.

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