The jet energy scale and its systematic uncertainty are determined for jets measured with the ATLAS detector at the LHC in proton-proton collision data at a centre-of-mass energy of root s = 7 TeV corresponding to an integrated luminosity of 38 pb(-1). Jets are reconstructed with the anti-k(t) algorithm with distance parameters R = 0.4 or R = 0.6. Jet energy and angle corrections are determined from Monte Carlo simulations to calibrate jets with transverse momenta pT >= 20 GeV and pseudorapidities vertical bar eta vertical bar < 4.5. The jet energy systematic uncertainty is estimated using the single isolated hadron response measured in situ and in test-beams, exploiting the transverse momentum balance between central and forward jets in events with dijet topologies and studying systematic variations in Monte Carlo simulations. The jet energy uncertainty is less than 2.5 % in the central calorimeter region (vertical bar eta vertical bar < 0.8) for jets with 60 <= p(T) < 800 GeV, and is maximally 14 % for p(T) < 30 GeV in the most forward region 3.2 <= vertical bar eta vertical bar < 4.5. The jet energy is validated for jet transverse momenta up to 1 TeV to the level of a few percent using several in situ techniques by comparing a well-known reference such as the recoiling photon p(T), the sum of the transverse momenta of tracks associated to the jet, or a system of low-p(T) jets recoiling against a high-p(T) jet. More sophisticated jet calibration schemes are presented based on calorimeter cell energy density weighting or hadronic properties of jets, aiming for an improved jet energy resolution and a reduced flavour dependence of the jet response. The systematic uncertainty of the jet energy determined from a combination of in situ techniques is consistent with the one derived from single hadron response measurements over a wide kinematic range. The nominal corrections and uncertainties are derived for isolated jets in an inclusive sample of high-p(T) jets. Special cases such as event topologies with close-by jets, or selections of samples with an enhanced content of jets originating from light quarks, heavy quarks or gluons are also discussed and the corresponding uncertainties are determined.