The university was created by a committee led by Thomas Burns, and officially established by an ordinance of the Otago Provincial Council in 1869. The university accepted its first students in July 1871, making it the oldest university in New Zealand and the third-oldest in Oceania. Between 1874 and 1961 the University of Otago was a part of the federal University of New Zealand and issued degrees in its name.

Otago is known for its vibrant student life, particularly its flatting, which is often in old houses. Otago students have a long-standing tradition of naming their flats. The nickname for Otago students "Scarfie" comes from the habit of wearing a scarf during the cold southern winters. but the term "Breathers", a corruption of "brothers", is now common. The university's graduation song, Gaudeamus igitur, iuvenes dum sumus ("Let us rejoice, while we are young"), acknowledges students will continue to live up to the challenge, if not always in the way intended. The university's student magazine, Critic, is New Zealand's longest-running student magazine.

The architectural grandeur and accompanying gardens of Otago University led to it being ranked as one of the world's most beautiful university campuses by the British newspaper The Daily Telegraph and the American online news website The Huffington Post.