We describe the partial cranium and skeleton of a new diprotodontian marsupial from the late Oligocene (~26-25 Ma) Namba Formation of South Australia. This is one of the oldest Australian marsupial fossils known from an associated skeleton and it reveals previously unsuspected morphological diversity within Vombatiformes, the clade that includes wombats (Vombatidae), koalas (Phascolarctidae) and several extinct families. Several aspects of the skull and teeth of the new taxon, which we refer to a new family, are intermediate between members of the fossil family Wynyardiidae and wombats. Its postcranial skeleton exhibits features associated with scratch-digging, but it is unlikely to have been a true burrower. Body mass estimates based on postcranial dimensions range between 143 and 171 kg, suggesting that it was ~5 times larger than living wombats. Phylogenetic analysis based on 79 craniodental and 20 postcranial characters places the new taxon as sister to vombatids, with which it forms the superfamily Vombatoidea as defined here. It suggests that the highly derived vombatids evolved from wynyardiid-like ancestors, and that scratch-digging adaptations evolved in vombatoids prior to the appearance of the ever-growing (hypselodont) molars that are a characteristic feature of all post-Miocene vombatids. Ancestral state reconstructions on our preferred phylogeny suggest that bunolophodont molars are plesiomorphic for vombatiforms, with full lophodonty (characteristic of diprotodontoids) evolving from a selenodont morphology that was retained by phascolarctids and ilariids, and wynyardiids and vombatoids retaining an intermediate selenolophodont condition. There appear to have been at least six independent acquisitions of very large (>100 kg) body size within Vombatiformes, several having already occurred by the late Oligocene.