A friend confirmed Simon Nellist died in the attack on Wednesday.
Police have not yet formally identified the victim and his family have not commented.
Australian authorities are still searching for the great white shark, with swimmers banned from the water and most city beaches shut after Wednesday's attack.
Mr Nellist - who was a diving instructor - was mauled by a great white shark just off Little Bay in east Sydney. He was a member of the city's Scuba Diving Social Club and a regular swimmer at the beach, BBC Sydney correspondent Shaimaa Khalil reports.
A UK foreign office spokesperson said consular staff were in touch with New South Wales Police. "We are supporting the family of a British man and our thoughts are with them at this difficult time," the spokesperson said.
Shark attacks in Sydney are uncommon because the city has long had nets and other deterrents in its waters.
On Thursday, surf lifesavers on jet skis patrolled a 25km (15.5 mile) stretch of water from Bondi in the city's east to Cronulla in the south to find the shark. Authorities are also using helicopters and drones.
The state government said its shark experts had estimated the predator to be a great white shark "at least three metres" in length based on footage of the incident taken by a member of the public.