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The 18-year-old driver of the vehicle, also a former Waitaki Boys' pupil, was seriously injured in the crash and remains in Dunedin Hospital.
The Otago Daily Times does not know the identity of the second victim.
Fire crews found the car alight when they arrived at the scene at the intersection of TY Duncan and Shortland Rds about 11pm on Wednesday. Two bodies were discovered inside.
Waitaki Boys' rector Darryl Paterson said pupils and staff were distraught when they learned a former year 12 pupil, who recently left the school, was killed in the crash.
"It's been a shock to everybody, and not what you expect as the day starts.
"The boy who was killed in the crash was a good friend of many of the boys and obviously they are very upset about it.
"He was an engaging student ... he was a very good friend and always prepared to help out his friends."
Mr Paterson said that he last saw the pupil last week when the boy stepped in to help one of the school's junior basketball teams which had been struggling for numbers.
"That's the sort of boy he was."
Asked if the school planned to hold a memorial service, he said news of the boy's death was "too fresh" and the school was focusing on supporting pupils and staff.
Detective Sergeant Hannah Booth, of Oamaru, said the circumstances that led to the crash had yet to be established.
"We still don't know the possible factors yet," she said.
"We are still speaking to witnesses and finding out what's actually occurred."
Yesterday had "just been about the scene examination and recovering the victims, so that is what our priority has been".
The road remained closed for more than 12 hours after the crash.
The light-coloured car appeared to have run off the roughly 2km Shortland Rd and collided with large stones at the gate of a TY Duncan Rd property.
The car was covered and hoisted on to the back of a flat-deck truck before being taken away.
The serious crash unit finished its investigation about 12.45pm and the road was reopened.
Scorch marks remained on the stones and some glass on the road.
The occupant of the TY Duncan Rd property declined to comment.
A Southern District Health Board spokeswoman said the driver remained in Dunedin Hospital in a stable condition.
Waitaki Mayor Gary Kircher said he expected the community would rally around the families of those involved in the crash.
"It's a very terrible time for the family and friends of the victims and our thoughts go out to them," Mr Kircher said.
"It's time for the community to get in behind the people that have been really affected by this and give them their full support."