It is believed Briton Simon Nellist, 35, was training for a forthcoming charity swim when he was fatally attacked in front of horrified onlookers in on Wednesday afternoon.
His family released a tribute calling him a "wonderful human being" and "very talented photographer".
"Simon was a gentle, kind and wonderful human being. He was a cherished fiancee, son, brother, uncle and friend," they told the BBC.
"Simon was funny, compassionate and always had time for people. He had a rare gift of instantly being able to connect with others, gaining their trust and respect."
Nellist's family said he was a "proud Cornishman" who had made Australia his home with his fiancee Jessie.
"Simon had a great passion for nature and the sea, as well as being a very talented photographer," they said.
Friends described Nellist, an experienced diving instructor as someone who "loved the water".
Della Ross, a friend of 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 Nellist as "such a nice guy".
Emergency services were called to Little Bay at around 4.35pm local time on Wednesday after reports that a swimmer had been attacked by a shark.
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.
It is believed Nellist was training for the five kilometre Malabar Ocean Swim, due to take place this weekend, when he was killed.
The event has been cancelled as a mark of respect, organisers said.
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