The 36-year-old was in the sea off the popular beach of Brisants de Saint-Gilles when a shark charged at him twice, prompting a nearby swimmer to raise the alert when he saw blood on the water, the local prefecture said.
Lifeguards jumped in the water to fetch the victim, who had lost a lot of blood and was in cardiac and respiratory arrest. They brought him back to the beach but were unable to revive him.
The shark had bitten the surfer on the arm and on the thigh. His wife was on the beach when the attack happened, and is being treated for shock, authorities said.
The deadly shark attack was the first this year on the island, where three people were killed by sharks in the past two years.
Last summer, another surfer in the Reunion island was attacked by a shark that tore off his arm and leg, although he survived.
Sharks are not man-eaters, but sometimes mistake humans for their natural prey, like seals or tortoises, and at other times hurt surfers as they "mouth" them out of curiosity, experts say.
Last year, 78 shark attacks were reported around the world, of which eight were fatal.
The series of shark attacks in the Reunion island has seen a number of measures implemented. Local authorities have initiated several scientific studies to try and better understand the way of life of the animals.
People have also been deployed near beaches on boats or in the water to keep an eye on swimmers and surfers and spot sharks before they attack.