Physics-based models of volcanic eruptions can directly link magmatic processes with diverse, time-varying geophysical observations, and when used in an inverse procedure make it possible to bring all available information to bear on estimating properties of the volcanic system. We develop a technique for inverting geodetic, extrusive flux, and other types of data using a physics-based model of an effusive silicic volcanic eruption to estimate the geometry, pressure, depth, and volatile content of a magma chamber, and properties of the conduit linking the chamber to the surface. A Bayesian inverse formulation makes it possible to easily incorporate independent information into the inversion, such as petrologic estimates of melt water content, and yields probabilistic estimates for model parameters and other properties of the volcano. Probability distributions are sampled using a Markov-Chain Monte Carlo algorithm. We apply the technique using GPS and extrusion data from the 2004–2008 eruption of Mount St. Helens. In contrast to more traditional inversions such as those involving geodetic data alone in combination with kinematic forward models, this technique is able to provide constraint on properties of the magma, including its volatile content, and on the absolute volume and pressure of the magma chamber. Results suggest a large chamber of >40 km3 with a centroid depth of 11–18 km and a dissolved water content at the top of the chamber of 2.6–4.9 wt%.