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He was Russell "Rusty" McDonald, 67, of Oamaru.
On behalf of his family, police expressed their gratitude to the search teams involved in locating Mr McDonald.
Mr McDonald’s death has been referred to the coroner.
His body was discovered before noon on Saturday after an extensive search of a large section of the river started on Friday afternoon.
The incident was reported to emergency services about 2.25pm, after three people had gone into the water when the jet-boat they were fishing in flipped near Black Point, about 53km northwest of Oamaru.
Sergeant Tony Woodbridge, of Oamaru, said the incident happened about 11am, but the alarm was not raised for more than three hours, as it took the two people who swam to shore some time to reach a farmhouse on foot, where they were able to contact emergency services.
On Saturday morning police confirmed that a body had been found near Black Point and that a formal identification and postmortem would take place.
Earlier, a helicopter crew joined Friday's search shortly before 3pm, and a land search and rescue operation, based at the Duntroon Domain and involving more than a dozen people from North Otago Search and Rescue and Upper Waitaki Search and Rescue, started late on Friday afternoon.
A dive team from Dunedin had also joined the search party and four jet-boats scoured the river for several hours, before the search was put on hold about 8pm.
Police also conducted a short search around the Waitaki River mouth.
The jet-boat was located in the river late on Friday.
It was not clear how the boat had capsized, Sgt Woodbridge said.
On Saturday morning, jet-boats from the Duntroon area and Dunedin LandSAR members joined the search, which resumed at 7am before search teams were stood down when the man's body was discovered before noon.
A police spokesman said the two people who made their way to shore were taken to Oamaru Hospital by ambulance in a moderate condition.