Abstract: This paper presents the first observation of top-quark pair production in association with two photons (t (t) over bar gamma gamma). The measurement is performed in the single-lepton decay channel using proton-proton collision data collected by the ATLAS detector at the Large Hadron Collider. The data correspond to an integrated luminosity of 140 fb(-1) recorded during Run 2 at a centre-of-mass energy of 13 TeV. The t (t) over bar gamma gamma production cross section, measured in a fiducial phase space based on particle-level kinematic criteria for the lepton, photons, and jets, is found to be 2.42(-0.53)(+0.58) fb, corresponding to an observed significance of 5.2 standard deviations. Additionally, the ratio of the production cross section of t (t) over bar gamma gamma. to top-quark pair production in association with one photon is determined, yielding (3.30(-0.65)(+0.70)) x 10(-3).