He will also become the dean of Te Tumu, the university's School of Maori, Pacific and Indigenous Studies, taking up the post in February 2009.
Dr Tapsell, who is in France, was until recently the Tumuaki Maori (Maori director) at Auckland Museum.
He comes from well-known whanau who trace their descent from the main tribes of Te Arawa, and has a distinguished academic record, university officials say.
He has a BA degree and MA (the latter with first-class honours) in anthropology from Auckland University and has been an adjunct senior lecturer in anthropology at that university.
He also has an Oxford doctorate.
His wife, Dr Merata Kawharu (Ngati Whatua), is a former Rhodes Scholar and also has an Oxford doctorate.
She is the research director of the James Henare Maori Research Centre at Auckland University.
Otago vice-chancellor Prof David Skegg said Te Tumu would flourish under Dr Tapsell's leadership, and the university already had a strong base in Maori studies.
Te Tumu's former head, Prof Tania Ka'ai, resigned last year during a university inquiry into her conduct as an employee, and now holds a professorship at AUT, in Auckland.
She had claimed to have been constructively dismissed from Otago University and unjustifiably disadvantaged by the way the investigation was conducted.
University human resources director Kevin Seales said the university had always been confident its actions had been entirely appropriate throughout.
Because Prof Ka'ai had withdrawn her claims, which were to have been considered at a public hearing of the Employment Relations Authority in Dunedin last month, the hearing would not be held, and the university could not disclose details of the case, he said.
Associate Prof Michael Reilly will continue as acting head of Te Tumu for the rest of this year.
The advisory committee for the chair's appointment also recommended that Prof Reilly should be appointed to a personal chair in Maori, Pacific and Indigenous Studies.
Prof Reilly, a specialist on Maori tribal history and the history of other indigenous peoples of the Pacific, joined the Otago staff in 1991.