WELLINGTON (REUTERS) - Three men miraculously survived after their helicopter crashed into the freezing sub-Antarctic waters off New Zealand's southern tip by swimming to shore at night and camping on an island for hours until they were rescued.

Helicopter pilot Andrew Hefford, paramedic John Lambeth and winchman Lester Stevens were recovering at a hospital after they were found on Tuesday (April 23) on an island about 450km south of New Zealand, according to statements from the Rescue Coordination Centre NZ.

The helicopter disappeared on Monday near the Auckland Islands en route to a medical evacuation off a fishing vessel.

The Coordination Centre began search operations shortly after receiving a report of the missing aircraft, but there was little hope of finding survivors due to the ice cold waters and deteriorating weather conditions in the Southern Ocean.

Five fishing vessels worked throughout the night, searching the area, the Centre said.

One of the survivors, Mr Stevens, told online news portal Stuff that he was knocked unconscious when the aircraft hit the water.

He recalled swimming to land on his back and kicking, and remembered Mr Lambeth and Mr Hefford dragging him out of the water.

Once on land, they built a hut and waited to be rescued.

The trio would have swam about 20 minutes to reach to the shore, the New Zealand Herald reported.

"You know, we just did what we did and survived," Mr Stevens told Stuff.

A fishing boat spotted a door from the helicopter the next day and soon after, the trio were spotted walking on a beach, the Coordination Centre said.

"We were ecstatic," Mr Sean Mullally, one of the pilots who was part of the rescue mission, told Radio New Zealand.

"It was unbelievable to see them still alive. It was a great moment."

Mr Mullally said the three were easy to spot on the islands as they were wearing big orange jackets.

Rescue Coordination Centre NZ duty manager Kevin Banaghan said in a statement that the helicopter crew were trained for emergency situations and were wearing cold water immersion suits.

The suits can sustain people in water temperatures as low as minus 30 deg C.

Southern Lakes Helicopters, which owns the downed aircraft, said an investigation would be needed to find out why the emergency locator beacons on the helicopter failed, Radio New Zealand reported.

Southern Lakes chief executive and chief pilot Richard Hayes said finding the three men alive was a highlight of his career.

"We ended up with the best result you can imagine," he told Radio New Zealand.