Dr Cox (25), a former Otago Daily Times Class Act award winner who graduated with MB ChB with distinction in medicine and surgery from Otago University last year, said gaining the scholarship was "incredibly humbling".
The university's tradition of success in the scholarship reflected the positive mix of cultural and sporting activities that was an important part of the wider life of the university, Dr Cox said.
He plans to take up his scholarship mid next year, and will undertake a DPhil in cardiovascular medicine. He begins work on Monday in Greymouth as a surgical house surgeon.
A former head boy at Otago Boys High School, he was ranked in the top 10 in the Commonwealth for the decathlon in 2006.
Miss Fraser, who was educated at James Hargest High School in Invercargill, was "shocked but also excited" by her success.
Otago University's history of success in gaining the scholarship showed that "Otago produces more than just academics", with graduates also emerging as "well-rounded" people, she said.
A "nice" part of the success was that she would also be able to join her partner, Jesse Wall, also an Otago graduate, who won a Rhodes Scholarship last year.
Miss Fraser, a former Invercargill hockey representative and an accomplished debater, has just completed an LLB (hons) and BA in politics at Otago.
She will pursue studies at Oxford towards a bachelor of civil law, followed by a master of science in environmental change and management.
Nina Hall, an Auckland University political studies graduate, was also selected for next year's Rhodes Scholarship.
