The structure of Mercury's internal magnetic field has been determined from analysis of orbital Magnetometer measurements by the MESSENGER spacecraft. We identified the magnetic equator on 531 low-altitude and 120 high-altitude equator crossings from the zero in the radial cylindrical magnetic field component,Bρ. The low-altitude crossings are offset 479 ± 6 km northward, indicating an offset of the planetary dipole. The tilt of the magnetic pole relative to the planetary spin axis is less than 0.8°. The high-altitude crossings yield a northward offset of the magnetic equator of 486 ± 74 km. A field with only nonzero dipole and octupole coefficients also matches the low-altitude observations but cannot yield off-equatorialBρ= 0 at radial distances greater than 3520 km. We compared offset dipole and other descriptions of the field with vector field observations below 600 km for 13 longitudinally distributed, magnetically quiet orbits. An offset dipole with southward directed moment of 190 nT-RM3yields root-mean-square (RMS) residuals below 14 nT, whereas a field with only dipole and octupole terms tuned to match the polar field and the low-altitude magnetic equator crossings yields RMS residuals up to 68 nT. Attributing the residuals from the offset-dipole field to axial degree 3 and 4 contributions we estimate that the Gauss coefficient magnitudes for the additional terms are less than 4% and 7%, respectively, relative to the dipole. The axial alignment and prominent quadrupole are consistent with a non-convecting layer above a deep dynamo in Mercury's fluid outer core.