The inclusive and fiducial tt¯ production cross-sections are measured in the lepton+jets channel using 20.2fb-1 of proton–proton collision data at a centre-of-mass energy of 8 TeV recorded with the ATLAS detector at the LHC. Major systematic uncertainties due to the modelling of the jet energy scale and b-tagging efficiency are constrained by separating selected events into three disjoint regions. In order to reduce systematic uncertainties in the most important background, the W+,jets process is modelled using Z+ jets events in a data-driven approach. The inclusive tt¯ cross-section is measured with a precision of 5.7% to be σinc(tt¯)=248.3±0.7(stat.)±13.4(syst.)±4.7(lumi.)pb, assuming a top-quark mass of 172.5 GeV. The result is in agreement with the Standard Model prediction. The cross-section is also measured in a phase space close to that of the selected data. The fiducial cross-section is σfid(tt¯)=48.8±0.1(stat.)±2.0(syst.)±0.9(lumi.)pb with a precision of 4.5%.