Charged-particle spectra obtained in Pb+Pb interactions at root s(NN) = 2.76TeV and pp interactions at root s(NN) = 2.76TeV with the ATLAS detector at the LHC are presented, using data with integrated luminosities of 0.15 nb(-1) and 4.2 pb(-1), respectively, in a wide transverse momentum (0.5 < p(T) < 150 GeV) and pseudorapidity (vertical bar eta vertical bar < 2) range. For Pb+Pb collisions, the spectra are presented as a function of collision centrality, which is determined by the response of the forward calorimeters located on both sides of the interaction point. The nuclear modification factors R-AA and R-CP are presented in detail as a function of centrality, p(T) and eta. They show a distinct p(T)-dependence with a pronounced minimum at about 7 GeV. Above 60 GeV, R-AA is consistent with a plateau at a centrality-dependent value, within the uncertainties. The value is 0.55 +/- 0.01(stat.) +/- 0.04(syst.) in the most central collisions. The R-AA distribution is consistent with flat vertical bar eta vertical bar dependence over the whole transverse momentum range in all centrality classes.