Using 1.8  fb-1 of pp collisions at a center-of-mass energy of 7 TeV recorded by the ATLAS detector at the Large Hadron Collider, we present measurements of the production cross sections of Υ(1S,2S,3S) mesons. Υ mesons are reconstructed using the dimuon decay mode. Total production cross sections for pT<70  GeV and in the rapidity interval |yΥ|<2.25 are measured to be, 8.01±0.02±0.36±0.31  nb, 2.05±0.01±0.12±0.08  nb, and 0.92±0.01±0.07±0.04  nb, respectively, with uncertainties separated into statistical, systematic, and luminosity measurement effects. In addition, differential cross section times dimuon branching fractions for Υ(1S), Υ(2S), and Υ(3S) as a function of Υ transverse momentum pT and rapidity are presented. These cross sections are obtained assuming unpolarized production. If the production polarization is fully transverse or longitudinal with no azimuthal dependence in the helicity frame, the cross section may vary by approximately ±20%. If a nontrivial azimuthal dependence is considered, integrated cross sections may be significantly enhanced by a factor of 2 or more. We compare our results to several theoretical models of Υ meson production, finding that none provide an accurate description of our data over the full range of Υ transverse momenta accessible with this data set.