The first observation of the $t\overline{t}H$ process in a single Higgs boson decay channel with the full reconstruction of the final state ($H\ensuremath{\rightarrow}\ensuremath{\gamma}\ensuremath{\gamma}$) is presented, with a significance of 6.6 standard deviations ($\ensuremath{\sigma}$). The $CP$ structure of Higgs boson couplings to fermions is measured, resulting in an exclusion of the pure $CP$-odd structure of the top Yukawa coupling at $3.2\ensuremath{\sigma}$. The measurements are based on a sample of proton-proton collisions at a center-of-mass energy $\sqrt{s}=13\text{ }\text{ }\mathrm{TeV}$ collected by the CMS detector at the LHC, corresponding to an integrated luminosity of $137\text{ }\text{ }{\mathrm{fb}}^{\ensuremath{-}1}$. The cross section times branching fraction of the $t\overline{t}H$ process is measured to be ${\ensuremath{\sigma}}_{t\overline{t}H}{\mathcal{B}}_{\ensuremath{\gamma}\ensuremath{\gamma}}={1.56}_{\ensuremath{-}0.32}^{+0.34}\text{ }\text{ }\mathrm{fb}$, which is compatible with the standard model prediction of ${1.13}_{\ensuremath{-}0.11}^{+0.08}\text{ }\text{ }\mathrm{fb}$. The fractional contribution of the $CP$-odd component is measured to be ${f}_{CP}^{Htt}=0.00\ifmmode\pm\else\textpm\fi{}0.33$.