The measurement of Higgs boson production in association with a top quark-antiquark pair in the diphoton decay channel ($H \to \gamma \gamma$) is presented, based on the analysis of 139~fb$^{-1}$ of proton-proton collision data with center-of-mass energy $\sqrt{s}=13$ TeV recorded with the ATLAS detector at the Large Hadron Collider. The analysis is performed using a simultaneous fit in seven signal-enriched event categories. The $t\bar{t}H$ process is observed in the diphoton decay mode with a significance of 4.9 standard deviations relative to the background-only hypothesis. The expected significance is 4.2 standard deviations. The $t\bar{t}H$ cross-section times the $H \to \gamma \gamma$ branching ratio is measured to be $\sigma_{t\bar{t}H}\times B_{\gamma\gamma} = 1.59_{-0.39}^{+0.43}$~fb, in agreement with the Standard Model prediction.

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