The top anti-top quark production cross-section is measured in the lepton+jets channel using proton–proton collision data at a centre-of-mass energy of s=13 TeV collected with the ATLAS detector at the LHC. The dataset corresponds to an integrated luminosity of 139 fb−1. Events with exactly one charged lepton and four or more jets in the final state, with at least one jet containing b-hadrons, are used to determine the tt¯ production cross-section through a profile-likelihood fit. The inclusive cross-section is measured to be σinc=830±0.4(stat.)±36(syst.)±14(lumi.)pb with a relative uncertainty of 4.6%. The result is consistent with theoretical calculations at next-to-next-to-leading order in perturbative QCD. The fiducial tt¯ cross-section within the experimental acceptance is also measured.