New Zealand-born Steven Payne, 37, was attacked at a remote beach about noon (local time) on Monday at Wharton Beach, east of Esperance in Western Australia.
A large sea and coastal search failed to find his remains and WA police on Wednesday said it had been suspended "pending any new information being received".
Payne, his partner and dog were five weeks into a six-month caravan trip around the western half of Australia when the incident happened, according to his family.
"Steve was one of the best. A gentle giant at 6ft4 (193cm), he was smart, kind, funny, laid back and very practical," Payne's family said in a statement.
"While he wasn't a man of many words, he loved his partner deeply, cherished his family, thought the world of his best mates, and was devoted to his dog."
Payne was raised just outside Wellington, and his love of surfing began in Dunedin while he was studying at the University of Otago, 1News reported.
“He was a volunteer firefighter with the CFA near where he and his partner and dog lived in Geelong and a well-respected colleague," the family said.
“Steven Payne was a beloved partner, son, brother, uncle, nephew, cousin and friend.”
Drone footage from a witness of the attack showed a shark swimming away from a large cloud of blood close to the shore and a surfboard with bite marks was recovered from the water.
Payne was about 50m offshore in chest-deep water with two other surfers when he was attacked, The New Zealand Herald reports.
Police said his partner witnessed the incident, "which is tragic".
The presumed death is the fourth fatal shark attack since 2017 in the area, about 800km south of Perth.
The family said Payne, who lived in Geelong, Victoria, would not have supported a shark cull or any attempt to kill the shark responsible.
"He and his partner spent a lot of time in the ocean together, had enjoyed many dives with sharks and knew the risks."
- AAP/ALP
