Debate is ongoing as to which tectonic model is most consistent with the known geology of southeast Australia, formerly part of the eastern margin of Gondwana. In particular, numerous tectonic models have been proposed to explain the enigmatic geological relationship between Tasmania and the mainland, which is separated by Bass Strait. One of the primary reasons for the lack of certainty is the limited exposure of basement rocks, which are masked by the sea and thick Mesozoic–Cenozoic sedimentary and volcanic cover sequences. We use ambient noise tomography recorded across Bass Strait to generate a new shear wave velocity model in order to investigate crustal structure. Fundamental mode Rayleigh wave phase velocity dispersion data extracted from long-term cross-correlation of ambient noise data are inverted using a transdimensional, hierarchical, Bayesian inversion scheme to produce phase velocity maps in the period range 2–30 s. Subsequent inversion for depth-dependent shear wave velocity structure across a dense grid of points allows a composite 3-D shear wave velocity model to be produced. Benefits of the transdimensional scheme include a data-driven parametrization that allows the number and distribution of velocity unknowns to vary, and the data noise to also be treated as an unknown in the inversion. The new shear wave velocity model clearly reveals the primary sedimentary basins in Bass Strait as slow shear velocity zones which extend down to 14 km in depth. These failed rift basins, which formed during the early stages of Australia–Antarctica break-up, appear to be overlying thinned crust, where high velocities of 3.8–4.0 km s⁻¹ occur at depths greater than 20 km. Along the northern margin of Bass Strait, our new model is consistent with major tectonic boundaries mapped at the surface. In particular, we identify an east dipping velocity transition zone in the vicinity of the Moyston Fault, a major tectonic boundary between the Lachlan and Delamerian orogens, which are part of the Phanerozoic accretionary terrane that makes up eastern Australia. A pronounced lineament of high shear wave velocities (∼3.7–3.8 km s⁻¹) in the lower crust of our new model may represent the signature of relict intrusive magmatism from failed rifting in the early stages of Australia–Antarctica break-up along a crustal scale discontinuity in the Selwyn Block microcontinent which joins Tasmania and Victoria.