The inclusive J/ψ production cross-section and fraction of J/ψ mesons produced in B-hadron decays are measured in proton-proton collisions at √s=7 TeV with the ATLAS detector at the LHC, as a function of the transverse momentum and rapidity of the J/psi, using 2.3pb−1 of integrated luminosity. The cross section is measured from a minimum pT of 1 GeV to a maximum of 70 GeV and for rapidities within |y|<2.4 giving the widest reach of any measurement of J/ψ production to date.