We present a baseline, time-averaged model for Mercury's magnetosphere, derived from MESSENGER Magnetometer data from 24 March to 12 December 2011, comprising the spacecraft's first three Mercury years in orbit around the innermost planet. The model, constructed under the approximation that the magnetospheric shape can be represented as a paraboloid of revolution, includes two external (magnetopause and magnetotail) current systems and an internal (dipole) field and allows for reconnection. We take advantage of the geometry of the orbital Magnetometer data to estimate all but one of the model parameters, and their ranges, directly from the observations. These parameters are then used as a priori constraints in the paraboloid magnetospheric model, and the sole remaining parameter, the dipole moment, is estimated as 190 nTRM3from a grid search. We verify that the best fit dipole moment is insensitive to changes in the other parameters within their determined ranges. The model provides an excellent first-order fit to the MESSENGER observations, with a root-mean-square misfit of less than 20 nT globally. The results show that the magnetopause field strength ranges from 10% to 50% of the dipole field strength at observation locations on the dayside and at nightside latitudes north of 60°N. Globally, the residual signatures observed to date are dominated by the results of magnetospheric processes, confirming the dynamic nature of Mercury's magnetosphere.