Charged Higgs bosons heavier than the top quark and decaying via H± → tb are searched for in proton-proton collisions measured with the ATLAS experiment at (Formula presented.) TeV corresponding to an integrated luminosity of 20.3fb−1. The production of a charged Higgs boson in association with a top quark, gb → tH±, is explored in the mass range 200 to 600 GeV using multi-jet final states with one electron or muon. In order to separate the signal from the Standard Model background, analysis techniques combining several kinematic variables are employed. An excess of events above the background-only hypothesis is observed across a wide mass range, amounting to up to 2.4 standard deviations. Upper limits are set on the gb → tH± production cross section times the branching fraction BR(H± → tb). Additionally, the complementary s-channel production, qq′ → H±, is investigated through a reinterpretation of W′ → tb searches in ATLAS. Final states with one electron or muon are relevant for H± masses from 0.4 to 2.0 TeV, whereas the all-hadronic final state covers the range 1.5 to 3.0 TeV. In these search channels, no significant excesses from the predictions of the Standard Model are observed, and upper limits are placed on the qq′ → H± production cross section times the branching fraction BR(H± → tb).