Subducted slab roll-back, lithospheric instability and asthenospheric extrusion have all been proposed as mechanisms that explain the evolution of the extensional Pannonian Basin, within the convergent arc of the Alpine–Carpathian mountain system in central Europe. We determine the P- and S-wave velocity structure of the mantle to depths of 850 km beneath this region using tomographic inversion of relative arrival-time residuals from 225 (P waves) and 124 (S waves) teleseismic earthquakes recorded by 56 stations of the Carpathian Basins Project (CBP) temporary seismic network (16-month duration) and 44 permanent seismic stations. The observed median P-wave relative arrival-time residuals vary between −1.13 s (early) in the Alps and 1.12 s (late) at the western end of the Carpathians; S-wave relative arrival-time residuals are about twice as large (−2.13 s and 3.39 s). We tested the effect of deterministic corrections on our relative arrival-time residuals using crustal velocity models from controlled source experiments, but show that the use of station terms in the inversion provides a robust method of correcting for near-surface crustal variation. Our tomographic models reduce the P-wave rms residual by 71 per cent to 0.130 s and our S-wave rms residual by 59 per cent to 0.624 s. At shallow sublithospheric depths we image several localized lower velocity regions, correlated with higher heat flow and interpreted as upwelling asthenosphere. We image a high velocity structure down to depths of about 350 km beneath the Eastern Alps. Further east, beneath the Pannonian Basin, a deeper continuation of the Eastern Alps fast anomaly is imaged trending E–W from ∼300 km depth and extending into the mantle transition zone (MTZ). In the MTZ we image a fast anomaly extending outwards as far as the Carpathians, the Dinarides and the Eastern Alps. This higher velocity mantle material is interpreted as being produced by a mantle downwelling, whose detachment from the lithosphere above may have triggered the extension of the Pannonian Basin.