Doreen Collyer, a university lecturer originally from Chester, Cheshire, was attacked on Sunday while diving off Mindarie Beach, north of Perth, the Daily Mail reported.
Police Inspector Danny Mulligan said the 60-year-old's dive partner managed to pull her out of the water after she was attacked but her injuries proved fatal, according to the Associated Press.
Her dive partner, who has been named only as John, said that he felt something brush past him but when he surfaced he realised Collyer had been attacked.
ABC said that fishermen who came to the pair’s assistance claimed to have seen a shark longer than their 5.3m (18ft) fishing boat.
The beach has now been closed and Western Australia’s Fishers Department is hunting the animal.
The Mail reported that fisheries metropolitan regional manager Tony Cappelluti said that any shark caught following Collyer’s death would be shot.
A video taken in the same area just hours after the attack appeared to show a "huge" shark.
In the footage, a fin can be seen in the water while a voice can be heard saying "that was huge!".
Collyer’s husband David paid tribute to her, saying: "Doreen was a beautiful person and everyone loved her. She was a devoted grandmother, mother and loving wife.”
The couple, who have two children and one grandchild, moved to Australia five years ago to be closer to their son and granddaughter, the Mail reported.
Collyer had recently become an Australian citizen, according to ABC.
Her dive partner also described her as a "phenomenal diver".
Although she was an advanced open water diver, it is understood that she had not been out diving for a number of weeks when the tragedy took place.
Collyer was the second person killed by a shark in Western Australia in less than a week. On Tuesday, a surfer's leg was bitten off by a shark about 60 miles (100km) south of where the Collyer was mauled.
Ben Gerring, 29, later died of his injuries.
A 4.2m shark was caught and killed following the attack.