"Sir John provided strong support to the University of Canterbury, especially in the years since the 2010/2011 earthquakes," Wood said.
"His leadership has been critical to the rebuild, not just on campus but in the region in general, and we will be eternally grateful to him for that.
"He has also been a supporter of the university in a personal capacity and I sincerely hope that his connection with this institution will continue and strengthen in time to come."
Key told the Herald he had no plans to use the title "Dr".
"It's not my intention to use the title as it's my view that honorary doctorates are ceremonial and to use the title could both be misleading but could take away from those who have worked so hard to earn a PhD."
The honorary doctorate has special significance, Key said, both because he attended the University of Canterbury, but also because of the impact that the Canterbury earthquakes had on the university.
Key was made a Knight Grand Companion of the New Zealand Order of Merit in June. And last month he was appointed an Honorary Companion in the Order of Australia - the highest ranked grade in the order.
Key's honorary degree is the latest to be bestowed on former politicians. Former Prime Minister Jim Bolger received an honorary doctorate of literature from Massey University. He also received an honorary doctorate from Khon Kaen University in Thailand.