Horatio Chapple, 17, was participating in an expedition organized by the British Schools Exploration Society, The Independent reported. He was a student at Eton, one of Britain's premier schools.
Those injured included two team leaders and two high school students, officials said. After they were evacuated from the Von Postbreen Glacier, they were flown from Longyearbyen, the principal settlement in the archipelago, to the mainland.
"We got a call via satellite phone from a British group of campers that there had been a polar bear attack and that one person was dead and that others were injured and they needed assistance," said Liv Asta Odegaard, spokeswoman for the Svalbard governor. "There are no roads in the area so we scrambled a helicopter."
Polar bears are common in Svalbard, where local residents carry rifles when they leave settled areas. Attacks are frequent but fatalities are unusual, with only four reported since 1971.
Ilona Wisniewska of the Svalbard tourism board said when bears attack they are usually shot before they have the chance to hurt more than one or two people.