Ambient seismic noise tomography has proven to be a valuable tool for imaging 3D crustal shear velocity using surface waves; however, conventional two-stage inversion schemes are severely limited in their ability to properly quantify solution uncertainty and account for inhomogeneous data coverage. In response to these challenges, we developed a two-stage hierarchical, transdimensional, Bayesian scheme for inverting surface wave dispersion information for a 3D shear velocity structure and apply it to ambient seismic noise data recorded in Tasmania, southeast Australia. The key advantages of our Bayesian approach are that the number and distribution of model parameters are implicitly controlled by the data and that the standard deviation of the data noise is treated as an unknown in the inversion. Furthermore, the use of Bayesian inference — which combines prior model information and observed data to quantify the a posteriori probability distribution — means that model uncertainty information can be correctly propagated from the dispersion curves to the phase velocity maps and finally onward to the 1D shear models that are combined to form a composite 3D image. We successfully applied the new method to ambient noise dispersion data (1–12-s period) from Tasmania. The results revealed an east-dipping anomalously low shear velocity zone that extends to at least a 15-km depth and can be related to the accretion of oceanic crust onto the eastern margin of Proterozoic Tasmania during the mid-Paleozoic.