Mercury Psillakis, 57, had been alerting other surfers to the large shark before he was mauled at Long Reef Beach in northern Sydney on Saturday.
"Merc is and will always be a hero, a loving and devoted husband, father and family man who could bring humour to every situation," his wife Maria and daughter Freedom said in a statement released on Tuesday.
"We are devastated by this loss, but will forever carry his spirit, energy and joy in our hearts."
Surfing was "one of his greatest passions" and he mastered the waves on his board on a daily basis, they said.
"He was always vigilant about keeping himself safe," the family said.
"Unfortunately, this was a tragic and unavoidable accident."
Long Reef and adjacent Dee Why beaches reopened on Tuesday for the first time since the fatal attack.
Lifeguards continued to monitor the water and conduct patrols using jetskis, with swimmer safety remaining the top priority, the local council said.
Beaches in Manly and Freshwater were closed briefly on Monday after an offshore shark detection.
The weekend's fatal attack, the first recorded on the northern beaches in nine decades, has scuppered a planned removal of shark nets at three NSW beaches.
Premier Chris Minns on Tuesday drew a line through the trial proceeding this season, after discussions with Agriculture Minister Tara Moriarty over the weekend.
"We're not going to be removing nets as part of a trial this summer," he said on Tuesday.
"That would be a silly decision to make in light of this tragedy."
Some 51 nets, each stretching 150 metres and sitting metres below the surface, are installed at beaches between Newcastle and Wollongong, including Dee Why, throughout spring and summer.
Councils on Sydney's northern beaches and eastern suburbs and the NSW Central Coast had been supportive of the trial but refused to nominate a beach, saying the state government should make the call.
Brianna Le Busque, an environmental science researcher at the University of South Australia, argued the move was an unfortunate, knee-jerk response.
"Shark nets are not an effective mitigation approach, and can actually provide ocean users with false security that they are being protected from bites," she said.
"We know that people fear things that we feel we can't control, and non-effective mitigation techniques like nets can make people inaccurately feel in control of shark interactions."
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