The top-photon electromagnetic couplings can be probed via the analysis of the production of top quark pairs (tt̅) in association with a photon (γ). A dataset of events with final-states containing jets, missing transverse momentum, one isolated electron or muon and an energetic photon is selected out of 4.59±0.08 1/fb of proton--proton collisions at a centre-of-mass energy of 7 TeV recorded by the ATLAS detector at the CERN Large Hadron Collider. In total 140 and 222 tt̅γ candidate events are observed in the electron and muon channels, respectively. They are to be compared to an expectation of 79 ± 26 and 120 ± 39 background events in the single-electron and single-muon channels respectively. A first observation of tt̅γ state, combining both electron and muon channels, is reported, with tt̅γ events being separated by 5.3 standard deviations from the background only hypothesis. The tt̅γ production cross section times the branching ratio (BR) of the single-lepton decay channel, as well as its spectrum in transverse energy of the photon, are measured in a fiducial phase-space within the detector acceptance. The measured cross section is σ(tt̅γ)× BR = 63 ±8 (stat.) +17 -13 (syst.) ± 1 (lumi.) fb per lepton flavour, which is in good agreement with the leading-order theoretical calculation normalised to the next-to-leading-order theoretical prediction of 48 ± 10 fb.