The complex tectonic setting of the central‐western Mediterranean has interested geoscientists for decades, but its geodynamic evolution remains a matter of debate. We rely on 807 seismometers from southern Europe and northern Africa to measure Rayleigh and Love phase velocities in the period range ∼5–200 s, based on teleseismic earthquakes and seismic ambient noise. By nonlinear joint inversion of the phase‐velocity maps, we obtain a 3‐D shear‐wave velocity (VS) model of the study area. At shallow depths, our model correlates with surface geology and reveals the presence of a sedimentary cover in the Liguro‐Provençal basin, as opposed to the Tyrrhenian basin where this is either very thin or absent. At ∼5‐km depth, high velocities below the Magnaghi, Vavilov, and Marsili seamounts point to an exhumed, scarcely serpentinized mantle. These are replaced by lower velocities at larger depths, likely connected to the presence of partial melt. At 50–60‐km depth, a very heterogeneous structure characterizes the Tyrrhenian basin, with low velocities pointing to the presence of fluids due to the lateral mantle inflow from the Ionian slab edges, and higher velocities associated with a relatively dry upper mantle. Such heterogeneity disappears at depths ≳75 km, replaced by more uniform velocities which are ∼2% lower than those found in the Liguro‐Provençal basin. We infer that, at the same depths, the Tyrrhenian basin is characterized by a larger concentration of fluids and possibly higher temperatures.