A direct search for lepton-flavour-violating decays of a Higgs boson ($m_{\textrm{H}}$ = 125 GeV) is described. The search is performed for the $\textrm{H} \rightarrow \textrm{e} \tau_{\mu}$, $\textrm{H} \rightarrow \textrm{e} \tau_{h}$, and $\textrm{H} \rightarrow \textrm{e} \mu$ decays, where $\tau_{h}$ and $\tau_{\mu}$ are taus reconstructed in the hadronic and muonic decay channels, respectively. The data sample used in the search corresponds to an integrated luminosity of $19.7$ fb$^{-1}$ collected in pp collisions at $\sqrt{s}=8$ TeV with the CMS experiment at the CERN LHC. No evidence is found for lepton-flavour-violating decays in either final state. For the $\textrm{H} \rightarrow \textrm{e} \tau_{\mu}$ and $\textrm{H} \rightarrow \textrm{e} \tau_{h}$ channels, the sensitivity of the search is an order of magnitude better than the existing indirect limits. A constraint of $B(\textrm{H} \rightarrow \textrm{e} \tau )<0.70\%$ at 95$\%$ confidence level is set. We also set a limit on the branching ratio of $B(\textrm{H} \rightarrow \textrm{e} \mu)$ $< 0.036\%$ at 95$\%$ confidence level. The limits on $B(\textrm{H} \rightarrow \textrm{e} \tau )$ and $B(\textrm{H} \rightarrow \textrm{e} \mu)$ are subsequently used to constrain the $|Y_{\textrm{e}\tau}|$ and $|Y_{\textrm{e}\mu}|$ Yukawa couplings.

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