We present the result of a 3-D gravity and P-wave traveltime joint inversion applied to the hydrothermal system of La Soufri'ere of Guadeloupe. The joint inversion process is used here to overcome the different resolution limitations attached to the two data sets. P-wave traveltimes were obtained from three active seismic surveys that were conducted from 2001 to 2007. Gravity data collected during a microgravity campaign is described in a companion paper. We use a joint inversion process based on a Bayesian formulation and a deterministic iterative approach. The coupling between slowness and density is introduced through a supplementary constraint in the misfit function that tries to minimize the distance between parameter values and a theoretical relationship. This relationship is derived from measurements on samples representative of Mt Pel'ee of Martinique and La Soufri'ere volcanoes. We chose a grid discretization that leads to an under-determined problem that we regularize using spatial exponential covariance between the nodes parameters. Our results are compared to geophysical electromagnetic results obtained using resistivity and VLF surveys. They confirm the presence of highly contrasted dense/fast and light/slow zones in La Soufri'ere dome and crater basement. Our images suggest however that some non-conductive zones may be massive andesite bodies rather than argilized zones, and that these bodies may have deeper roots than hypothesized.