They have been named as Daniel Thomas Hollnsteiner, 21, from New York, USA and James Robert Murphy, 20, from London, England.
Police confirmed the men and the nine people who survived after a kayaking expedition went wrong were students attending Monash University in Melbourne, Australia and were visiting New Zealand during a semester break.
The three other members of the groups who were admitted to Hospital last night will released from the Timaru Hospital later this afternoon.
Inquiries into the event will continue over the weekend and the matter will be referred to the coroner.
The British Foreign and Commonwealth Office released a statement saying it was supporting the man's family and was in contact with New Zealand authorities.
The Melbourne-based university said this morning it had sent a "senior officer" to support the group staying in South Canterbury.
"Our deepest sympathies are extended to the families , friends and colleagues during this tragic time," Monash said in a statement.
"Monash is liaising directly with the students and officials here in Australia and in New Zealand, to provide support," the University added.
The kayakers were part of an 11-member group aged in their early 20s who were travelling around New Zealand in campervans and had arranged to meet at the lake for the day.
Kylee Smith, AquaNorts' co-owner, called 111. She said everyone connected with the group was devastated after the two young people died.
"Our main concern is for the families of the survivors and the families of these people."
She said an investigation would probably shed more light on what went wrong and she could not comment in detail.
"It is an absolutely tragic event, and our hearts go out to everybody involved. It's tragic for us and for them - and our hearts and our thoughts are with the families."
Lake Tekapo Scenic Resort manager Wayne Hardaker said the lake was like "glass" in the morning but changed rapidly.
Mr Hardaker understood somebody at the kayak hire company first called 111.
Nine people survived after local volunteers and emergency services workers rescued them.
"It could have been a lot worse," Mr Hardaker said.
He believed an AquaNorts employee went out to try and help the group.
"...He noticed that the lake got very choppy, and tried to go out there, and the boat couldn't go out, because it was just too rough."
Mr Hardaker said the glacier-fed lake was almost always frigid. He said even on midsummer days with 30-degree temperatures, the lake was so cold "you could only stay in five minutes.
Monash University said it would offer counselling for any students or staff who asked for it.
The other nine were rescued by locals and emergency service staff and treated for hypothermia. Three were taken by ambulance to Timaru Hospital, two in a serious condition. Last night, their condition had improved to stable.
Police area commander Inspector Dave Gaskin said when the group first went out on the lake, the weather was calm. But they were hit by winds gusting up to 40kmh.
"The boats were swamped and they were tipped into the water. The air temperature when it happened was about 3 degrees and the water wasn't much warmer than that and they were in the water for about an hour," he said.
"I think all of them are very lucky to be alive. To spend that amount of time in water that cold is pretty difficult."
The group, all wearing life-jackets, were kayaking around the lake unguided and had gone too far from shore.
Mr Gaskin said emergency services were alerted about 4.30pm. A local man who had hired out the kayaks made the call after seeing the change in weather.
"He tried to go out in the boat, but the waves were too high."
Mr Gaskin wouldn't say if the two deaths were due to hypothermia.
He said some of the group were able to scramble ashore on nearby Motuariki Island and start a fire to keep warm. Others made it ashore to the banks of Lake McGregor.
Local volunteers and emergency service workers picked up the nine kayakers and retrieved the two bodies.
Mr Gaskin said the survivors would stay the night in Timaru.
"They are obviously extremely distressed."
He said it was not unheard of for the weather to change so quickly.
"Lake Tekapo is very dangerous."
Godley Hotel duty manager Rey Mendoza said he was alerted to the tragedy by a flurry of sirens. Five ambulances were on the lakeshore and a helicopter was coming and going.
A local resident said the wind was very strong in the afternoon and the lake had been extremely rough.
The Lake Tekapo area, about 245km southwest of Christchurch, is famous for recreation activities such as tramping, mountain biking, fishing, hunting, boating and skiing.
- Additional reporting NZ Herald
