It is believed Simon Nellist, 35, who has not yet been formally identified, was training for a charity swim when he was attacked in front of horrified onlookers in Sydney’s Little Bay on Wednesday afternoon.
Friends described Mr Nellist, an experienced diving instructor who was engaged to be married, as someone who “loved the water”.
A search is continuing for the rest of his remains and the shark that killed him.
Mr Nellist, from Penzance in Cornwall, had served with the UK's Royal Air Force as an engineer. He moved to Australia after he took a holiday to the country, according to reports.
Tributes have flooded in for the victim, both in Australia and in the country of his birth.
Della Ross, a friend of Mr Nellist, told broadcaster 7News: “Everything that is connected to Simon, to me is connected to the ocean.
“The news hit us like a truck because he is really one of the people that makes this Earth better.”
A neighbour living in the Wolli Creek area of Sydney described Mr Nellist as “such a nice guy”.
One of his former neighbours in the UK said his death was a tragedy for his family.
He told the Daily Mail: “He was a nice guy, a big, strapping bloke and at that time he was an engineer in the RAF. When I saw his name on the news I wondered whether it was the same guy.”
The incident, believed to be the first fatal shark attack in Sydney since 1963, prompted the immediate closure of more than a dozen beaches in the area until Friday.
A spokesman for the Department of Primary Industries said: “Based on footage provided by the public, including eyewitness accounts, DPI shark biologists believe that a white shark, at least three metres in length, was likely responsible.”
It is believed Mr Nellist was training for the 5k Malabar Magic Ocean Swim, due to take place this weekend, when he was killed.
The event has been cancelled as a mark of respect, organisers said.
An event statement read: “The organising committee extend our thoughts and prayers to the family of the swimmer who was so tragically taken yesterday.
“Out of respect for the swimmer and his family, and following wide consultation with Randwick Council and experienced, senior Surf Life Saving personnel, we believe that cancelling the 2022 swim is appropriate.”