Laetitia Brouwer, 17, was pulled to shore with critical injuries on Monday and died later in hospital.
The family say they are “heartbroken” but take comfort knowing she died “doing something she loved”.
Laetitia was surfing with her father at Kelp Beds at Wylie Bay, a few miles from Esperance, when she was attack at around 4pm local time (10am BST).
Family spokesman Steve Evans read a statement to the media at a conference in Esperance, saying Laeticia's death had left her family devastated.
He said: “Laeticia will be greatly missed by her family, friends and everyone who knew her.”
The teenager died while surfing with family during an Easter break
Esperance police’s Acting Senior Sergeant Ben Jeffes confirmed the family was “not a long way off shore” and described the teenager's death as “an absolute tragedy”, adding the victim’s father did everything he could to save his daughter's life.
He added: "Father and daughter were surfing out at where the waves are breaking and that's where the attack occurred, and the father obviously tried everything he could to help his daughter but sadly he wasn't able to save her.”
St John Ambulance said paramedics arrived on the scene 19 minutes after they were called, but the teenager's injuries were severe, with reports suggesting she lost a leg during the attack.
The State Government has confirmed drum lines were not deployed following the attack to try to catch the shark using baited hooks, claiming it was too late in the day but the beach remained closed.
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Following the fatality, the Government is now reviewing the "serious threat" guidelines established by the Barnett government and hopes to announce its policy in the coming weeks.
Department of Fisheries spokesman Russell Adams said it was likely a great white was responsible.
He said: “Researchers have had a look at the photo of the surfboard and on that basis alone they can't tell what sort of shark it is.
"Since 2000 all fatal attacks in WA have been caused by great whites, so you could assume safely it was a great white.”
He added shark sightings were not uncommon in the area, but there was no research to suggest it was more dangerous to swim or surf there, compared to other locations in Western Australia.
Reports suggest the victim lost a leg during attack
There have been 15 fatal shark attacks in the state since 2000, with Laeticia’s death the third fatality in the area in less than a year.
Marc Payne – a seasoned abalone diver in Esperance – said the number of great white sharks in the area had grown.
He said: "I've had quite an increase in interactions with white sharks of around about 200 per cent in the past three decades.
"Most of the interactions I'm getting are from the smaller size juvenile and teenage type animals."