The complex H2SO4-H2O has been observed by rotational spectroscopy in a supersonic jet. A-type spectra for 18 isotopic forms have been analyzed, and the vibrationally averaged structure of the system has been determined. The complex forms a distorted, six-membered ring with the water unit acting as both a hydrogen bond donor and a hydrogen bond acceptor toward the sulfuric acid. One of the H2SO4 protons forms a short, direct hydrogen bond to the water oxygen, with an H···O distance of 1.645(5) Å and an O-H···O angle of 165.2(4)°. Additionally, the orientation of the water suggests a weaker, secondary hydrogen bond between one of the H2O hydrogens and a nearby S=O oxygen on the sulfuric acid, with an O···H distance of 2.05(1) Å and an O-H ···O angle of 130.3(5)°. The experimentally determined structure is in excellent agreement with previously published DFT studies. Experiments with HOD in the jet reveal the formation of only isotopomers involving deuterium in the secondary hydrogen bond, providing direct experimental evidence for the secondary H···O interaction. Extensive isotopic substitution has also permitted a re-determination of the structure of the H2SO4 unit within the complex. The hydrogen-bonding OH bond of the sulfuric acid elongates by 0.07(2) Å relative to that in free H2SO4, and the S=O bond involved in the secondary interaction stretches by 0.04(1) Å. These changes reflect substantial distortion of the H2SO4 moiety in response to only a single water molecule, and prior to the proton transfer event. Spectral data indicate that the complex undergoes at least one, and probably more than one type of internal motion. Although the sulfuric acid in this work was produced from direct reaction of SO3 and water in the jet, experiments with H218O indicate that about 2-3% of the acid is formed via processes not normally associated with the gas-phase hydration of SO3.