Dr Aguirre, who studied the dolphin as part of his PhD research, said that like most living dolphins, Papahu had many simple conical teeth, but its head was probably a bit wider, and not as high-domed.
It lived at a time of global warmth, in shallow seas around Zealandia - or proto-New Zealand - along with ancient penguins and baleen whales.
Zealandia, the New Zealand continent, is a large fragment of the former super-continent of Gondwana that sits between the Pacific and Indian-Australian Plates and is nearly completely submerged by water.
The skull, one jaw, and a few other parts of Papahu taitapu were found in marine sedimentary rocks in the Cape Farewell region of northern South Island.
The researchers used the Maori name taitapu to honour this region, and Papahu is a Maori name for dolphin.
Only a single specimen had been found so far and the fossil is housed in the university's Geology Museum.
"Our study of structures of the skull and earbone suggest that Papahu could make and use high frequency sound to navigate and detect prey in murky water," Dr Aguirre said.
"They probably also used sound to communicate with each other."
Features of the Papahu skull can be used to analyse relationships with other dolphins and toothed whales.
That work showed that the skull was distinct from all previously-reported fossils, which is why the dolphin could be formally named as a new form, he said.
"When we compared Papahu with both modern and fossil dolphins we found that it belongs in a diverse and structurally variable group of ancient dolphins that evolved and spread world-wide 19 - 35 million years ago," Professor Fordyce said.
"All of those ancient dolphins including Papahu and others, such as shark-toothed dolphins, are now extinct.
"They have been replaced by the modern dolphins and toothed whales, which diversified within the last 19 million years."
It was not clear, however, exactly why Papahu and other ancient dolphins went extinct.
