The incident took place overnight in a camping area near the main town of Longyearbyen, located 1,300 kilometres from the North Pole.
The man, who has not been named, was seriously wounded during the attack and died soon after, the local governor's office said in a statement.
Other people at the scene fired shots at the bear, which was later found dead in the parking lot of the local airport. People on Svalbard are advised to carry a weapon when outside urban areas.
According to a tally from 2015, the archipelago is home to about 1,000 polar bears, a protected species since 1973.
Until now, five deadly attacks on people had been recorded since 1971.
The most recent one occurred in 2011 when a bear attacked a group of 14 people camping as part of a British school trip. A 17-year-old British student was killed and four others were injured before the animal was killed.
According to experts, the shrinking icecap has reduced the polar bears' preferred hunting grounds, where they eat seals, pushing them to approach populated areas in their hunt for food.