This letter reports the observation of W(ℓν)γγ production in proton-proton collisions. This measurement uses the full Run 2 sample of events recorded at a center-of-mass energy of s=13 TeV by the ATLAS detector at the LHC, corresponding to an integrated luminosity of 140 fb⁻¹. Events with a leptonically-decaying W boson and at least two photons are considered. The background-only hypothesis is rejected with an observed and expected significance of 5.6 standard deviations. The inclusive fiducial production cross section of W(eν)γγ and W(μν)γγ events is measured to be σfid=13.8±1.1(stat)+2.1−2.0(syst)±0.1(lumi) fb, in agreement with the Standard Model prediction.