The dynamics of mantle plumes and the origin of their associated swells remain some of the most controversial topics in geodynamics. Here we construct a numerical model of the mantle flow beneath the French Polynesia region. Our study is based on a new regional seismic tomography model, which high resolution allows obtaining information at the scale of plumes. We find excellent correlations between the observed and the modeled dynamic swells, between the modeled flow pattern and the active volcanism and between the buoyancy fluxes obtained from our numerical model and the ones deduced from the swells morphology. These outstanding fits reveal for the first time that a direct link exists between the surface observations and mantle flows.