Fossett, who ended a record-breaking solo round-the-world balloon flight this month, plans to co-pilot a glider to an altitude of 62,000 feet (18,900 metres), smashing the previous record of 48,228 feet (14,700 metres).
The tycoon will travel to the remote town of Omarama, east of the South Island's alpine ranges, where he and former US space agency (Nasa) test pilot Einar Enevoldson will ride "mountain waves" of wind into the stratosphere.
The flight is part of a project designed to better understand these waves, formed when strong winds flow over a mountain range.
Fossett, 58, and Enevoldson, 70, will attempt this record-breaking mission in a modified two-seat German glider. The craft's design should allow it to go higher than any previous models.
High speeds
"We spent two years modifying the glider. We want to fly high enough now that it's beyond previous technology in gliders," said Fossett.
Surfing the mountain waves is made more dangerous because of freezing temperatures and the need for speed in the altitude-thinned air.
The team's glider, which flies at around 90 km/h (56 mph) at sea level, must travel at 412 km/h (256 mph) to stay aloft at peak altitude, say experts.
If Fossett succeeds in breaking the current record, he will attempt the even headier height of 100,000 feet at a later date.
The US space agency is interested in this long-term goal because at this altitude, the air density is the same as on Mars.
"Nasa is very interested in finding out what kind of aircraft could fly on Mars and how to fly them," Fossett said.
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