Two of the men had not opened their chutes while the third appeared to have been opened too late. Michael McDowell, spokesman for Canadian firm Adventure Network International, which organised the pounds 13,000-a-head trip, said the dead parachutists were among a six-man team which had jumped at around 8,500 feet (2,600 metres) over the South Pole on Saturday.
"Three landed without problems but unfortunately two of the parachutes appear not to have deployed at all and one hardly deployed," said Mr McDowell. "This is a terrible tragedy and a mystery as all these men knew what they were doing and had taken every precaution."
He said they were all "vastly experienced" skydivers who had packed their own parachutes. Two of the three dead men had also jumped over the North Pole.
Two of the dead were American, aged 36 and 43, while the third was a 49-year-old Austrian.